• Search Research Projects
  • Search Researchers
  • How to Use
  1. Back to previous page

Comprehensive research of Einstein's equations based on analysis

Research Project

Project/Area Number 16H03940
Research Category

Grant-in-Aid for Scientific Research (B)

Allocation TypeSingle-year Grants
Section一般
Research Field Basic analysis
Research InstitutionOsaka University (2020, 2022)
Yamagata University (2016-2019)

Principal Investigator

Nakamura Makoto  大阪大学, 大学院情報科学研究科, 教授 (70312634)

Co-Investigator(Kenkyū-buntansha) 和田出 秀光  金沢大学, 機械工学系, 准教授 (00466525)
竹田 寛志  福岡工業大学, 工学部, 准教授 (10589237)
杉本 充  名古屋大学, 多元数理科学研究科, 教授 (60196756)
Project Period (FY) 2016-04-01 – 2021-03-31
Project Status Completed (Fiscal Year 2022)
Budget Amount *help
¥16,510,000 (Direct Cost: ¥12,700,000、Indirect Cost: ¥3,810,000)
Fiscal Year 2020: ¥2,990,000 (Direct Cost: ¥2,300,000、Indirect Cost: ¥690,000)
Fiscal Year 2019: ¥3,250,000 (Direct Cost: ¥2,500,000、Indirect Cost: ¥750,000)
Fiscal Year 2018: ¥3,250,000 (Direct Cost: ¥2,500,000、Indirect Cost: ¥750,000)
Fiscal Year 2017: ¥3,250,000 (Direct Cost: ¥2,500,000、Indirect Cost: ¥750,000)
Fiscal Year 2016: ¥3,770,000 (Direct Cost: ¥2,900,000、Indirect Cost: ¥870,000)
Keywords偏微分方程式 / 非線形 / 波動方程式 / 分散型方程式 / クライン・ゴルドン方程式 / アインシュタイン方程式 / 一様等方時空 / 初期値問題 / 大域可解性 / 爆発解 / 一様等方計量 / 漸近挙動 / プロカ方程式 / 偏微分方程式論 / 偏微分発定式 / ド・ジッター計量 / シュレディンガー方程式 / 一様等方空間 / 非線形場
Outline of Final Research Achievements

Field equations with nonlinear terms representing various self-interactions were considered in homogeneous and isotropic spacetimes considered in cosmology, and the theory of the well-posedness for initial value problems (unique existence of solutions, asymptotic behaviors of solutions, and existence of blowing-up solutions) has been constructed. In the process, we constructed linear and nonlinear estimates for partial differential equations in homogeneous and isotropic spacetimes. Through this study, we characterized the effects of the expansion or contraction of spaces using the theory of partial differential equations, and their effects on behaviors of solutions of nonlinear partial differential equations.

Academic Significance and Societal Importance of the Research Achievements

宇宙論におけるダークエネルギーが注目される中で、非線形偏微分方程式論においても、空間が膨張あるいは収縮する場合の方程式の解の挙動についての研究が、開拓的に発展している。べき乗型の非線形項を持つクライン・ゴルドン方程式の解の大域可解性の研究を中心として、指数関数型やハートリー型の非線形項も対象として、シュレディンガー方程式とマクスウェル方程式にも理論を展開した。空間の膨張あるいは収縮についての解析方法を構築する意義がある。

Report

(6 results)
  • 2022 Final Research Report ( PDF )
  • 2020 Annual Research Report
  • 2019 Annual Research Report
  • 2018 Annual Research Report
  • 2017 Annual Research Report
  • 2016 Annual Research Report
  • Research Products

    (154 results)

All 2021 2020 2019 2018 2017 2016 Other

All Int'l Joint Research (12 results) Journal Article (40 results) (of which Int'l Joint Research: 8 results,  Peer Reviewed: 39 results,  Open Access: 6 results,  Acknowledgement Compliant: 1 results) Presentation (96 results) (of which Int'l Joint Research: 49 results,  Invited: 68 results) Funded Workshop (6 results)

  • [Int'l Joint Research] Stanford University/The University of Texas RGV(米国)

    • Related Report
      2020 Annual Research Report
  • [Int'l Joint Research] Stanford University/University of Texas Rio Grande Valley(米国)

    • Related Report
      2019 Annual Research Report
  • [Int'l Joint Research] University of Bari(イタリア)

    • Related Report
      2019 Annual Research Report
  • [Int'l Joint Research] Imperial College London(英国)

    • Related Report
      2019 Annual Research Report
  • [Int'l Joint Research] The University of Texas(米国)

    • Related Report
      2018 Annual Research Report
  • [Int'l Joint Research] Stanford University(米国)

    • Related Report
      2018 Annual Research Report
  • [Int'l Joint Research] Peking University(中国)

    • Related Report
      2018 Annual Research Report
  • [Int'l Joint Research] Zhejiang University(中国)

    • Related Report
      2018 Annual Research Report
  • [Int'l Joint Research] The University of Texas(米国)

    • Related Report
      2017 Annual Research Report
  • [Int'l Joint Research] Peking University(中国)

    • Related Report
      2017 Annual Research Report
  • [Int'l Joint Research] TU Bergakademie Freiberg(Germany)

    • Related Report
      2016 Annual Research Report
  • [Int'l Joint Research] Zhejiang University(China)

    • Related Report
      2016 Annual Research Report
  • [Journal Article] On the Cauchy problem for the semilinear Proca equations in the de Sitter spacetime2021

    • Author(s)
      Nakamura, Makoto
    • Journal Title

      Journal of Differential Equations

      Volume: 270 Pages: 1218-1257

    • DOI

      10.1016/j.jde.2020.09.015

    • Related Report
      2020 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Scaling limit of modulation spaces and their applications2021

    • Author(s)
      M. Sugimoto, B. Wang
    • Journal Title

      Appl. Comput. Harmon. Anal.

      Volume: 53 Pages: 54-94

    • Related Report
      2020 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On an effect of inhomogeneous constraints for a maximizing problem of the Sobolev embedding associated with the space of bounded variation2021

    • Author(s)
      石渡通徳, 和田出秀光
    • Journal Title

      Studia Mathematica

      Volume: 257 Issue: 2 Pages: 213-240

    • DOI

      10.4064/sm190613-13-7

    • Related Report
      2020 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On the nonrelativistic limit of a semilinear field equation in a homogeneous and isotropic space2020

    • Author(s)
      M. Nakamura
    • Journal Title

      Kyoto Journal of Mathematics

      Volume: 60, No. 4,

    • Related Report
      2020 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Remarks on global solutions for the semilinear diffusion equation in the de Sitter spacetime2020

    • Author(s)
      M. Nakamura, Y. Sato
    • Journal Title

      Hokkaido Mathematical Journal

      Volume: 49

    • Related Report
      2020 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Remarks on the Navier-Stokes equations and the elastic wave equations in homogeneous and isotropic spacetimes2020

    • Author(s)
      M. Nakamura
    • Journal Title

      Tsukuba Journal of Mathematics

      Volume: 44, no. 2,

    • Related Report
      2020 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On some effects of background metrics for several partial differential equations2020

    • Author(s)
      M. Nakamura
    • Journal Title

      Advanced Studies in Pure Mathematics

      Volume: 85 Pages: 315-324

    • Related Report
      2020 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A trial to construct specific self-similar solutions to non-linear wave equations2020

    • Author(s)
      M. Sugimoto
    • Journal Title

      RIMS Kokyuroku Bessatsu

      Volume: B82 Pages: 177-182

    • Related Report
      2020 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Nonlinear operations on a class of modulation spaces2020

    • Author(s)
      Kato Tomoya、Sugimoto Mitsuru、Tomita Naohito
    • Journal Title

      Journal of Functional Analysis

      Volume: 278 Issue: 9 Pages: 108447-108447

    • DOI

      10.1016/j.jfa.2019.108447

    • Related Report
      2020 Annual Research Report 2019 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Spectral identities and smoothing estimates for evolution operators2020

    • Author(s)
      M. Ben-Artzi, M. Ruzhansky and M. Sugimoto
    • Journal Title

      Adv. Differential Equations

      Volume: 25 Pages: 627-650

    • Related Report
      2020 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Asymptotic behaviors of global solutions for a semilinear diffusion equation in the de Sitter spacetime2020

    • Author(s)
      Nakamura Makoto; Takeda, Hiroshi
    • Journal Title

      Asymptotic Analysis

      Volume: - Issue: 3-4 Pages: 203-245

    • DOI

      10.3233/asy-201652

    • Related Report
      2020 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Remarks on the derivation of several second order partial differential equations from a generalization of the Einstein equations2020

    • Author(s)
      M. Nakamura,
    • Journal Title

      Osaka J. Math.

      Volume: 57 Pages: 305-331

    • NAID

      120006846161

    • Related Report
      2019 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On the numerical analysis of the Cauchy problem for semilinear Klein-Gordon equations in the de Sitter spacetime2019

    • Author(s)
      T. Tsuchiya, M. Nakamura,
    • Journal Title

      Journal of Computational and Applied Mathematics

      Volume: 361 Pages: 396-412

    • Related Report
      2019 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On the regularity of the semilinear term on the Cauchy problem for the Schrodinger equation2019

    • Author(s)
      M. Nakamura,
    • Journal Title

      Proceedings of the 11th ISAAC congress 2017, Vaxjo (Sweden), Trends in Mathematics, Research Perspectives

      Volume: 00 Pages: 369-377

    • Related Report
      2019 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Global solutions for nonlinear Schrodinger equations in de Sitter spacetime2019

    • Author(s)
      M. Nakamura,
    • Journal Title

      Advanced Studies of Pure Mathematics, “Asymptotic Analysis for Nonlinear Dispersive and Wave Equations

      Volume: 81 Pages: 311-322

    • Related Report
      2019 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A local-to-global boundedness argument and Fourier integral operators2019

    • Author(s)
      M. Ruzhansky and M. Sugimoto
    • Journal Title

      J. Math. Anal. Appl.

      Volume: 473 Pages: 892-904

    • NAID

      120006643290

    • Related Report
      2019 Annual Research Report 2018 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Remarks on the Mizohata-Takeuchi conjecture and related problems2019

    • Author(s)
      N. Bez and M. Sugimoto
    • Journal Title

      Asymptotic Analysis for Nonlinear Dispersive and Wave Equations, Adv. Stud. Pure Math., Math. Soc. Japan, Tokyo

      Volume: 81 Pages: 1-12

    • Related Report
      2019 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Critical exponent for semi-linear wave equations with double damping terms in exterior domains2019

    • Author(s)
      D’Abbicco Marcello、Ikehata Ryo、Takeda Hiroshi
    • Journal Title

      Nonlinear Differential Equations and Applications NoDEA

      Volume: 26 Issue: 6 Pages: 25-25

    • DOI

      10.1007/s00030-019-0603-5

    • Related Report
      2019 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Strichartz type estimates in mixed Besov spaces with application to critical nonlinear Schrdinger equations2019

    • Author(s)
      M. Nakamura, T. Wada
    • Journal Title

      Journal of Differential Equations

      Volume: 印刷中

    • Related Report
      2018 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Remarks on global solutions for the semilinear diffusion equation in the de Sitter spacetime2019

    • Author(s)
      M. Nakamura, Y. Sato
    • Journal Title

      Hokkaido Mathematical Journal

      Volume: 印刷中

    • Related Report
      2018 Annual Research Report
    • Peer Reviewed
  • [Journal Article] The Cauchy problem for dissipative wave equations with weighted nonliner terms2019

    • Author(s)
      M. Nakamura, H. Wadade
    • Journal Title

      New Tools for Nonlinear PDEs and Application

      Volume: 印刷中

    • Related Report
      2018 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On the nonrelativistic limit of a semilinear field equation in a homogeneous and isotropic space2019

    • Author(s)
      M. Nakamura
    • Journal Title

      Kyoto Journal of Mathematics

      Volume: 印刷中

    • Related Report
      2018 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On the regularity of the semilinear term on the Cauchy problem for the Schroedinger equation2019

    • Author(s)
      M. Nakamura
    • Journal Title

      Proceedings of the 11th ISAAC congress 2017

      Volume: 印刷中

    • Related Report
      2018 Annual Research Report 2017 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Asymptotic profiles of solutions for structural damped wave equations2019

    • Author(s)
      Ryo Ikehata and Hiroshi Takeda
    • Journal Title

      J. Dynamics and Differential equations

      Volume: 31 Issue: 1 Pages: 537-571

    • DOI

      10.1007/s10884-019-09731-8

    • Related Report
      2018 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Large time behavior of global solutions to nonlinear wave equations with frictional and viscoelastic damping terms2019

    • Author(s)
      R. Ikehata, H. Takeda
    • Journal Title

      Osaka Journal of Mathematics

      Volume: 印刷中

    • NAID

      120006768703

    • Related Report
      2018 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Existence and non-existence of maximizers for the Moser-Trudinger type inequalities under inhomogeneous constraints2018

    • Author(s)
      Norihisa Ikoma, Michinori Ishiwata, Hidemitsu Wadade
    • Journal Title

      Mathematische Annalen (in press)

      Volume: in press Issue: 1-2 Pages: 831-851

    • DOI

      10.1007/s00208-018-1709-5

    • Related Report
      2019 Annual Research Report 2018 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] On the maximizing problem associated with Sobolev type embeddings under inhomogeneous constraints2018

    • Author(s)
      Michinori Ishiwata, Hidemitsu Wadade
    • Journal Title

      Applicable Analysis (in press)

      Volume: in press Issue: 10 Pages: 1-19

    • DOI

      10.1080/00036811.2018.1491971

    • Related Report
      2019 Annual Research Report 2018 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] On the eects of spatial expansion and contraction on several semilinear partial dierential equations2018

    • Author(s)
      M. Nakamura
    • Journal Title

      京都大学数理解析研究所講究録 ”非線形波動・分散型方程式”

      Volume: 2093 Pages: 27-37

    • Related Report
      2018 Annual Research Report
  • [Journal Article] Stability of Trace Theorems on the Sphere2018

    • Author(s)
      Neal Bez, Chris Jeavons, Tohru Ozawa, Mitsuru Sugimoto
    • Journal Title

      The Journal of Geometric Analysis

      Volume: 28 Issue: 2 Pages: 1456-1476

    • DOI

      10.1007/s12220-017-9870-8

    • NAID

      120006496423

    • Related Report
      2018 Annual Research Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] Some effects of the spatial variance on the Cauchy problem for partial differential equations2018

    • Author(s)
      M. Nakamura
    • Journal Title

      RIMS Kokyuroku Bessatsu

      Volume: 印刷中

    • Related Report
      2017 Annual Research Report 2016 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Unconditional small data global well-posedness for nonlinear beam equations with weak damping2018

    • Author(s)
      Hiroshi Takeda
    • Journal Title

      Nonlinear Analysis. Real World Applications

      Volume: 41 Pages: 1-33

    • DOI

      10.1016/j.nonrwa.2017.10.007

    • Related Report
      2017 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Uniform Energy Decay for Wave Equations with Unbounded Damping Coefficients2018

    • Author(s)
      R. Ikehata, H. Takeda
    • Journal Title

      Funkcialaj Ekvacioj

      Volume: 印刷中

    • NAID

      130007858187

    • Related Report
      2017 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Optimal constants and extremisers for some smoothing estimates2017

    • Author(s)
      Bez Neal、Sugimoto Mitsuru
    • Journal Title

      J. Anal. Math.

      Volume: 131 Issue: 1 Pages: 159-187

    • DOI

      10.1007/s11854-017-0005-8

    • Related Report
      2017 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] A natural approach to the asymptotic mean value property for the p-Laplacian2017

    • Author(s)
      Ishiwata Michinori、Magnanini Rolando、Wadade Hidemitsu
    • Journal Title

      Calculus of Variations and Partial Differential Equations

      Volume: 56 Issue: 4 Pages: 56-97

    • DOI

      10.1007/s00526-017-1188-7

    • NAID

      120006343950

    • Related Report
      2017 Annual Research Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] On the existence time of local solutions for critical semilinear Schroedinger equations in Sobolev spaces2017

    • Author(s)
      T. Iwabuchi, M. Nakamura
    • Journal Title

      Nonlinear Analysis: Real World Applications

      Volume: 33 Pages: 168-180

    • DOI

      10.1016/j.nonrwa.2016.06.009

    • Related Report
      2016 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Remarks on the Rellich inequality2017

    • Author(s)
      S. Machihara, T. Ozawa, H. Wadade
    • Journal Title

      Mathematische Zeitschrift

      Volume: 印刷中 Issue: 3-4 Pages: 1367-1373

    • DOI

      10.1007/s00209-016-1805-8

    • NAID

      120005982988

    • Related Report
      2016 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Smoothing estimates for non-dispersive equations2016

    • Author(s)
      M. Ruzhansky, M. Sugimoto
    • Journal Title

      Math. Ann.

      Volume: 365 Issue: 1-2 Pages: 241-269

    • DOI

      10.1007/s00208-015-1281-1

    • Related Report
      2016 Annual Research Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] Extremisers for the trace theorem on the sphere2016

    • Author(s)
      N. Bez, S. Machihara, M. Sugimoto
    • Journal Title

      Math. Res. Lett.

      Volume: 23 Issue: 3 Pages: 633-647

    • DOI

      10.4310/mrl.2016.v23.n3.a3

    • Related Report
      2016 Annual Research Report
    • Peer Reviewed / Int'l Joint Research / Acknowledgement Compliant
  • [Journal Article] A survey on optimal smoothing estimates and trace theorems2016

    • Author(s)
      N. Bez, M. Sugimoto
    • Journal Title

      Adv. Math.

      Volume: 45 Pages: 801-816

    • Related Report
      2016 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On the effect of equivalent constraints on a maximizing problem associated with the Sobolev type embeddings in R^N2016

    • Author(s)
      Michinori Ishiwata, Hidemitsu Wadade
    • Journal Title

      Mathematische Annalen

      Volume: 364 Issue: 3-4 Pages: 1043-1068

    • DOI

      10.1007/s00208-015-1243-7

    • NAID

      120005652940

    • Related Report
      2016 Annual Research Report
    • Peer Reviewed / Open Access
  • [Presentation] On the Klein-Gordon equation with the Hartree type semilinear term in the de Sitter spacetime2021

    • Author(s)
      M. Nakamura, H. Takashima
    • Organizer
      日本数学会年会
    • Related Report
      2020 Annual Research Report
  • [Presentation] A constructive approach to semilinear wave equations2021

    • Author(s)
      M. Sugimoto
    • Organizer
      Asia-Pacific Analysis and PDE seminar, オーストラリア・シドニー大学(オンライン)
    • Related Report
      2020 Annual Research Report
    • Invited
  • [Presentation] 準線形消散型弾性波方程式に対する初期値問題の時間大域解の挙動について2021

    • Author(s)
      H. Takeda
    • Organizer
      第38回九州における偏微分方程式研究集会
    • Related Report
      2020 Annual Research Report
    • Invited
  • [Presentation] On a construction of self-similar solutions to nonlinear wave equations2020

    • Author(s)
      M. Sugimoto
    • Organizer
      International Conference on Generalized Functions GF2020 (Plenary talk), ベルギー・ゲント大学(オンライン)
    • Related Report
      2020 Annual Research Report
    • Invited
  • [Presentation] 非線形波動方程式の自己相似解の構成法について2020

    • Author(s)
      M. Sugimoto
    • Organizer
      分散型方程式と実解析, 大阪大学(オンライン)
    • Related Report
      2020 Annual Research Report
    • Invited
  • [Presentation] Global solutions for the semilinear diffusion equation in the de Sitter spacetime2019

    • Author(s)
      M. Nakamura
    • Organizer
      The 12th International ISAAC Congress,'' Session ``Recent Progress in Evolution Equations,'' 2019年7月29日~8月2日, The University of Aveiro, Portugal.
    • Related Report
      2019 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Remarks on the Navier-Stokes equations in homogeneous and isotropic spacetimes2019

    • Author(s)
      M. Nakamura
    • Organizer
      ``The 12th International ISAAC Congress,'' Session ``Partial Differential Equations on Curved Spacetimes." 2019年7月29日~8月2日, The University of Aveiro, Portugal.
    • Related Report
      2019 Annual Research Report
    • Int'l Joint Research
  • [Presentation] On the semilinear partial differential equations in homogeneous and isotropic spacetimes2019

    • Author(s)
      M. Nakamura
    • Organizer
      Geometric Analysis and General Relativity, 2019年11月21日~23日, The University of Tokyo, Japan.
    • Related Report
      2019 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] On the Cauchy problem for a semilinear ordinary differential equation in homogeneous and isotropic spaces2019

    • Author(s)
      M. Nakamura
    • Organizer
      日本数学会,2019 年度秋季総合分科会,応用数学分科会,2019 年 9 月 17 日,金沢大学.
    • Related Report
      2019 Annual Research Report
  • [Presentation] On global solutions for the semilinear complex Ginzburg-Landau type equation in homogeneous and isotropic spaces2019

    • Author(s)
      M. Nakamura
    • Organizer
      日本数学会, 2019 年度秋季総合分科会,応用数学分科会, 2019 年 9 月 17 日,金沢大学.
    • Related Report
      2019 Annual Research Report
  • [Presentation] On the Cauchy problem for the Navier-Stokes equations in the de Sitter spacetime2019

    • Author(s)
      M. Nakamura
    • Organizer
      日本数学会, 2019 年度秋季総合分科会,実関数論分科会, 2019 年 9 月 20 日,金沢大学.
    • Related Report
      2019 Annual Research Report
  • [Presentation] Partial differential equations in homogeneous and isotropic spaces2019

    • Author(s)
      M. Nakamura
    • Organizer
      日本数学会, 2019 年度秋季総合分科会,実関数論分科会, 2019 年 9 月 20 日,金沢大学特別講演)
    • Related Report
      2019 Annual Research Report
    • Invited
  • [Presentation] On the Cauchy problem for the semilinear Proca equations in the de Sitter spacetime2019

    • Author(s)
      M. Nakamura
    • Organizer
      日本数学会, 2019 年度秋季総合分科会,函数方程式論分科会, 2019 年 9 月 20 日,金沢大学.
    • Related Report
      2019 Annual Research Report
  • [Presentation] Asymptotic profiles of global solutions for the semilinear diffusion equation in the de Sitter spacetime2019

    • Author(s)
      M. Nakamura, H. Takeda
    • Organizer
      日本数学会, 2019 年度秋季総合分科会,函数方程式論分科会, 2019 年 9 月 20 日,金沢大学.
    • Related Report
      2019 Annual Research Report
  • [Presentation] Some dissipative and anti-dissipative effects on semilinear PDEs in homogeneous and isotropic spaces2019

    • Author(s)
      M. Nakamura
    • Organizer
      三重偏微分方程式研究集会~西原健二先生の古希を記念して~, 2019 年 10 月 4 日, 三重大学.
    • Related Report
      2019 Annual Research Report
  • [Presentation] Remarks on the Navier-Stokes equations in homogeneous and isotropic spacetimes2019

    • Author(s)
      M. Nakamura
    • Organizer
      第21回「特異点と時空、および関連する物理」研究会, 2019年12月28日, カレッジプラザ, 秋田市.
    • Related Report
      2019 Annual Research Report
  • [Presentation] A specific construction of self-similar solutions for nonlinear wave equations2019

    • Author(s)
      M. Sugimoto
    • Organizer
      Regularity and Asymptotic Analysis for Critical Phenomena of Partial Differential Equations,京都大学数理解析研究所
    • Related Report
      2019 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Optimal trace theorems on the sphere and their stability2019

    • Author(s)
      M. Sugimoto
    • Organizer
      The 8th SEAMS-UGM International Conference on Mathematics and Its Applications (Plenary talk),インドネシア・Gadjah Mada 大,
    • Related Report
      2019 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] A trial to construct specific self-similar solutions for nonlinear wave equations2019

    • Author(s)
      M. Sugimoto
    • Organizer
      The 12th ISAAC Congress, ポルトガル・Aveiro 大
    • Related Report
      2019 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] On construction of self-similar solutions to nonlinear wave equations2019

    • Author(s)
      M. Sugimoto
    • Organizer
      Anomalies in Partial Differential Equations,イタリア・Roma 大INdAM
    • Related Report
      2019 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] On self-similar solutions to nonlinear wave equations2019

    • Author(s)
      M. Sugimoto
    • Organizer
      Function Spaces and Geometric Analysis and Their Applications,中国・南開大,
    • Related Report
      2019 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] On a construction of self-similar solutions to nonlinear wave equations2019

    • Author(s)
      M. Sugimoto
    • Organizer
      セミナー,中国・北京大学
    • Related Report
      2019 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] On a construction of self-similar solutions to nonlinear wave equations2019

    • Author(s)
      M. Sugimoto
    • Organizer
      セミナー,中国・中央財経大学
    • Related Report
      2019 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] 抽象的シュレディンガー発展作用素に関するあるスペクトル恒等式と比較原理2019

    • Author(s)
      M. Sugimoto
    • Organizer
      第19 回調和解析中央大セミナー
    • Related Report
      2019 Annual Research Report
    • Invited
  • [Presentation] On a maximizing problem for the Moser-Trudinger type inequality with inhomogeneous constraints2019

    • Author(s)
      Hidemitsu Wadade
    • Organizer
      6th Italian-Japanese Workshop "Geometric Properties for Parabolic and Elliptic PDE's," Cortona, Arezzo, Italy
    • Related Report
      2019 Annual Research Report
    • Int'l Joint Research
  • [Presentation] On a maximizing problem for the Moser-Trudinger type inequality with inhomogeneous2019

    • Author(s)
      Hidemitsu Wadade
    • Organizer
      12th International ISAAC Congress "Geometric and Regularity Properties of Solutions to Elliptic and Parabolic PDEs," Aveiro University, Aveiro, Portugal
    • Related Report
      2019 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Asymptotic profiles of solutions to semi-linear wave equations with structural damping2019

    • Author(s)
      Takeda Hiroshi
    • Organizer
      Workshop ``General Relativity and Partial Differential Equation'', 近畿大学
    • Related Report
      2019 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Remarks on lower bounds for the elastic wave with structural damping2019

    • Author(s)
      Takeda Hiroshi
    • Organizer
      長崎微分方程式セミナー, 長崎大学
    • Related Report
      2019 Annual Research Report
    • Invited
  • [Presentation] Asymptotic profiles of global solutions for the semilinear diffusion equation in the de Sitter spacetime2019

    • Author(s)
      中村 誠, 竹田 寛志
    • Organizer
      日本数学会2019年度秋季総合分科会関数方程式論分科会, 金沢大学
    • Related Report
      2019 Annual Research Report
  • [Presentation] 準線形弾性波の初期値問題に対する時間大域解の大域挙動について2019

    • Author(s)
      隠居 良行, 竹田 寛志
    • Organizer
      日本数学会2020年度年会関数方程式論分科会, 日本大学
    • Related Report
      2019 Annual Research Report
  • [Presentation] Remarks on a semilinear diffusion equation in homogeneous and isotropic spaces2019

    • Author(s)
      M. Nakamura
    • Organizer
      Top global university project, Waseda workshop on partial differential equations 2019
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Global solutions for the semilinear diffusion equation in the de Sitter spacetime2019

    • Author(s)
      M. Nakamura
    • Organizer
      Nonlinear Dispersive Equations in Kumamoto, 2019
    • Related Report
      2018 Annual Research Report
    • Invited
  • [Presentation] Partial dierential equations in uniform and isotropic spaces2019

    • Author(s)
      M. Nakamura
    • Organizer
      2018年度日本数学会東北支部会
    • Related Report
      2018 Annual Research Report
    • Invited
  • [Presentation] Global solutions for a semilinear diusion equation in expanding or contracting spaces2019

    • Author(s)
      M. Nakamura, Y. Sato
    • Organizer
      日本数学会年会
    • Related Report
      2018 Annual Research Report
  • [Presentation] On the Navier-Stokes equations in homogeneous and isotropic spacetimes with a constant density of mass2019

    • Author(s)
      M. Nakamura
    • Organizer
      日本数学会年会
    • Related Report
      2018 Annual Research Report
  • [Presentation] Asymptotic expansion of solutions for wave equations with structural damping and its application2019

    • Author(s)
      H. Takeda
    • Organizer
      Waseda Workshop on Partial Differential Equations 2019
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] On some effects of background metrics for several partial diffential equations2018

    • Author(s)
      M. Nakamura
    • Organizer
      The 11th Mathematical Society of Japan, Seasonal Institute
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] On the dissipative effect of the spatial expansion for the semilinear diffusion equation2018

    • Author(s)
      M. Nakamura
    • Organizer
      East Asian Conference in Harmonic Analysis and its Applications 2018
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] On the Navier-Stokes equation and the elastic wave equations in uniform and isotropic spaces2018

    • Author(s)
      M. Nakamura
    • Organizer
      Wayamba International Conference
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] On the global solutions for the semi-linear diffusion equation in de Sitter spacetime2018

    • Author(s)
      M. Nakamura and Y. Sato
    • Organizer
      Wayamba International Conference
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] The Cauchy problem for Navier-Stokes equations in de Sitter spacetime2018

    • Author(s)
      M. Nakamura
    • Organizer
      Workshop on Mathematical Sciences
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] The asymptotic behavior of the semi-linear diffusion equation in de Sitter spacetime2018

    • Author(s)
      M. Nakamura and Y. Sato
    • Organizer
      Workshop on Mathematical Sciences
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Spectral identities and smoothing estimates for evolution operators2018

    • Author(s)
      M. Sugimito
    • Organizer
      北京大学セミナー
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Remarks on nonlinear operations on modulation spaces2018

    • Author(s)
      M. Sugimito
    • Organizer
      Harmonic analysis and the Navier-Stokes equations(早稲田大学)
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Spectral identities and the comparison principle of smoothing estimates2018

    • Author(s)
      M. Sugimito
    • Organizer
      Modern problems of applied mathematics and information technologies(ウズベキスタン国立大)
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Spectral identities and the comparison principle of smoothing estimates for evolution equations2018

    • Author(s)
      M. Sugimito
    • Organizer
      Partial Differential Equation and General Relativity(名古屋大学)
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] 抽象的シュレディンガー方程式の初期値問題における平滑化評価式とその比較原理について2018

    • Author(s)
      M. Sugimito
    • Organizer
      解析セミナー(愛媛大学)
    • Related Report
      2018 Annual Research Report
    • Invited
  • [Presentation] Optimal trace theorems on the sphere2018

    • Author(s)
      M. Sugimito
    • Organizer
      The Legacy of Joseph Fourier after 250 years(中国・Tsinghua Sanya International Mathematics Forum)
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] 構造的消散項を持つ波動方程式の解の漸近展開とその応用について2018

    • Author(s)
      竹田寛志
    • Organizer
      熊本大学応用解析セミナー
    • Related Report
      2018 Annual Research Report
    • Invited
  • [Presentation] Remarks on the derivation of Navier-Stokes equations and elastic wave equations in uniform and isotropic spacetimes2018

    • Author(s)
      M. Nakamura
    • Organizer
      日本数学会年会, 東京大学.
    • Related Report
      2017 Annual Research Report
  • [Presentation] On the Cauchy problem of a semilinear diffusion equation in an expanding space2018

    • Author(s)
      M. Nakamura, Y. Sato
    • Organizer
      日本数学会年会, 東京大学.
    • Related Report
      2017 Annual Research Report
  • [Presentation] On the numerical stability of semi-linear Klein-Gordon equations in de Sitter spacetime2018

    • Author(s)
      M. Nakamura, T. Tsuchiya
    • Organizer
      日本数学会年会, 東京大学.
    • Related Report
      2017 Annual Research Report
  • [Presentation] A local-to-global boundedness argument and Fourier integral operators2018

    • Author(s)
      M. Sugimoto
    • Organizer
      Hyperbolic Partial Differential Equations and Related Topics, 中央大学
    • Related Report
      2017 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Optimal estimates of Kato--Yajima type with angular smoothing2018

    • Author(s)
      M. Sugimoto
    • Organizer
      偏微分方程式姫路研究集会, イーグレ姫路.
    • Related Report
      2017 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Asymptotic expansion of solutions to a nonlinear strong damped wave equation2018

    • Author(s)
      H. Takeda
    • Organizer
      Critical exponent and nonlinear evolution equations 2018, 東京理科大学.
    • Related Report
      2017 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Nonlinear field equations in the de Sitter spacetime and the Cauchy problem2017

    • Author(s)
      M. Nakamura
    • Organizer
      Seminar ``Phenomena and Differential Equations''
    • Place of Presentation
      山形大学(山形県)
    • Year and Date
      2017-03-21
    • Related Report
      2016 Annual Research Report
  • [Presentation] Complex Ginzburg-type equations with semilinear terms as the nonrelativistic limit of field equations2017

    • Author(s)
      M. Nakamura
    • Organizer
      Seminar ``Phenomena and Differential Equations''
    • Place of Presentation
      山形大学(山形県)
    • Year and Date
      2017-03-21
    • Related Report
      2016 Annual Research Report
  • [Presentation] On Klein-Gordon equations with power type and exponential type semilinear terms in moving spacetim2017

    • Author(s)
      M. Nakamura
    • Organizer
      研究会``Recent topics on Partial Differential Equations''
    • Place of Presentation
      山形大学(山形県)
    • Year and Date
      2017-03-09
    • Related Report
      2016 Annual Research Report
  • [Presentation] Dissipative effects of the cosmological constant on semilinear Schr\"odinger equations and parabolic equations2017

    • Author(s)
      M. Nakamura
    • Organizer
      研究会``Recent topics on Partial Differential Equations''
    • Place of Presentation
      山形大学(山形県)
    • Year and Date
      2017-03-09
    • Related Report
      2016 Annual Research Report
  • [Presentation] On the regularity of power type nonlinear term of the Schroedinger equation2017

    • Author(s)
      M. Nakamura
    • Organizer
      East Asian Conference in Harmonic Analysis and its Applications 2017, Zhejiang University of Science and Technology, China.
    • Related Report
      2017 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] The regularity of the semilinear term on the Cauchy problem for the Schroedinger equation2017

    • Author(s)
      M. Nakamura
    • Organizer
      The 11th ISAAC congress, Linnaeus University, Sweden.
    • Related Report
      2017 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Remarks on several second order partial differential equations and a generalization of the Einstein equation2017

    • Author(s)
      M. Nakamura
    • Organizer
      京都大学NLPDEセミナー, 京都大学.
    • Related Report
      2017 Annual Research Report
    • Invited
  • [Presentation] On the effects of spatial expansion and contraction on the semilinear Klein-Gordon equation2017

    • Author(s)
      M. Nakamura
    • Organizer
      研究集会"Nonlinear Wave and Dispersive Equations," 京都大学.
    • Related Report
      2017 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Dissipative effects of the spatial expansion for several PDEs2017

    • Author(s)
      M. Nakamura
    • Organizer
      研究集会「反応拡散方程式と非線形分散型方程式の解の挙動」, 京都大学.
    • Related Report
      2017 Annual Research Report
    • Invited
  • [Presentation] Remarks on the derivation of several partial differential equations2017

    • Author(s)
      M. Nakamura
    • Organizer
      研究集会``Recent Topics on Partial Differential Equations," 中央大学.
    • Related Report
      2017 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] On the Cauchy problem for semi-linear Klein-Gordon equations in de Sitter spacetime2017

    • Author(s)
      M. Nakamura
    • Organizer
      The 27th Workshop on General Relativity and Gravitation in Japan,東広島市くららホール.
    • Related Report
      2017 Annual Research Report
  • [Presentation] Remarks on semilinear field equations in uniform and isotropic spaces2017

    • Author(s)
      M. Nakamura
    • Organizer
      研究集会「微分方程式の総合的研究」, 東京工業大学.
    • Related Report
      2017 Annual Research Report
    • Invited
  • [Presentation] On the Cauchy problem for semi-linear field equations in de Sitter spacetime2017

    • Author(s)
      M. Nakamura
    • Organizer
      Lectures, School of Mathematical Sciences, 北京大学, 中国.
    • Related Report
      2017 Annual Research Report
    • Invited
  • [Presentation] On several partial differential equations in uniform and isotropic spaces2017

    • Author(s)
      M. Nakamura
    • Organizer
      研究集会「第19回特異点研究会」, 大阪市立大学.
    • Related Report
      2017 Annual Research Report
  • [Presentation] Remarks on nonlinear operations on modulation spaces2017

    • Author(s)
      M. Sugimoto
    • Organizer
      Aspects of Time-Frequency Analysis, イタリア.
    • Related Report
      2017 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Spectral comparison of smoothing estimates and its applications2017

    • Author(s)
      M. Sugimoto
    • Organizer
      8th International conference on Mathematical Modeling, ロシア.
    • Related Report
      2017 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Remarks on nonlinear operations on modulation spaces2017

    • Author(s)
      M. Sugimoto
    • Organizer
      Harmonic Analysis and its Applications in Tokyo 2017, 日本大学.
    • Related Report
      2017 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] 制限定理と関連する偏微分方程式論の諸問題2017

    • Author(s)
      M. Sugimoto
    • Organizer
      名古屋大学大学院多元数理科学研究科
    • Related Report
      2017 Annual Research Report
    • Invited
  • [Presentation] Spectral Comparison of Smoothing Estimates2017

    • Author(s)
      M. Sugimoto
    • Organizer
      The 11th ISAAC Congress, Sweden.
    • Related Report
      2017 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Trace theorems and related topics on PDE2017

    • Author(s)
      M. Sugimoto
    • Organizer
      Gadjah Mada 大学, インドネシア.
    • Related Report
      2017 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Spectral comparison of smoothing estimates2017

    • Author(s)
      M. Sugimoto
    • Organizer
      Recent Topics on Partial Differential Equations, 中央大学.
    • Related Report
      2017 Annual Research Report
    • Invited
  • [Presentation] 制限定理と関連する偏微分方程式論の諸問題2017

    • Author(s)
      M. Sugimoto
    • Organizer
      談話会, 広島大学.
    • Related Report
      2017 Annual Research Report
    • Invited
  • [Presentation] 構造的消散項をもつ波動方程式の解の大域挙動とその応用について2017

    • Author(s)
      H. Takeda
    • Organizer
      第2回大分解析セミナー, 福岡工業大学.
    • Related Report
      2017 Annual Research Report
    • Invited
  • [Presentation] 非線形強消散型波動方程式の時間大域解の挙動について2017

    • Author(s)
      H. Takeda
    • Organizer
      九州関数方程式セミナー, 福岡大学セミナーハウス.
    • Related Report
      2017 Annual Research Report
    • Invited
  • [Presentation] 強消散項を持つ非線形波動方程式の解の漸近形について2017

    • Author(s)
      H. Takeda
    • Organizer
      東北大学応用数学セミナー, 東北大学.
    • Related Report
      2017 Annual Research Report
    • Invited
  • [Presentation] Asymptotic expansion of the solution to a nonlinear wave equation with strong damping2017

    • Author(s)
      H. Takeda
    • Organizer
      解析セミナー, 神戸大学.
    • Related Report
      2017 Annual Research Report
    • Invited
  • [Presentation] Large time behavior of solutions to strong damped wave equations2017

    • Author(s)
      H. Takeda
    • Organizer
      The 11th ISAAC congress, Sweden.
    • Related Report
      2017 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Asymptotic profile of solutions to a nonlinear wave equation with strong damping2017

    • Author(s)
      H. Takeda
    • Organizer
      Ito Workshop on Partial Differential Equaions, 九州大学.
    • Related Report
      2017 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] On the derivation of several second order partial differential equations from the Einstein equation2017

    • Author(s)
      M. Nakamura
    • Organizer
      日本数学会年会
    • Place of Presentation
      首都大学東京(東京都)
    • Related Report
      2016 Annual Research Report
  • [Presentation] On the nonrelativistic limit of a semilinear field equation in uniform and isotropic space2017

    • Author(s)
      M. Nakamura
    • Organizer
      日本数学会年会
    • Place of Presentation
      首都大学東京(東京都)
    • Related Report
      2016 Annual Research Report
  • [Presentation] Spectral comparison of smoothing estimates and its applications2017

    • Author(s)
      M.Sugimoto
    • Organizer
      Critical Exponents and Nonlinear Evolution Equation 2017
    • Place of Presentation
      東京理科大学(東京都)
    • Related Report
      2016 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] On the derivation of a semilinear field equation in a uniform and isotropic space2016

    • Author(s)
      M. Nakamura
    • Organizer
      Wayamba International Conference
    • Place of Presentation
      Wayamba University of Sri Lanka, Sri Lanka
    • Year and Date
      2016-08-19
    • Related Report
      2016 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Optimal trace theorems and a related PDE problem2016

    • Author(s)
      M.Sugimoto
    • Organizer
      Fourier Analysis and Applications Workshop
    • Place of Presentation
      中国・Tsinghua Sanya International Mathematics Forum
    • Year and Date
      2016-08-15
    • Related Report
      2016 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Some effects of the spatial variance on the Cauchy problem for partial differential equations2016

    • Author(s)
      M. Nakamura
    • Organizer
      RIMS研究集会「調和解析と非線形偏微分方程式」
    • Place of Presentation
      京都大学(京都府)
    • Year and Date
      2016-07-04
    • Related Report
      2016 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] On a derivation of partial differential equations based on the relativistic theory2016

    • Author(s)
      M. Nakamura
    • Organizer
      信州大学偏微分方程式研究集会
    • Place of Presentation
      信州大学(長野県)
    • Year and Date
      2016-06-17
    • Related Report
      2016 Annual Research Report
    • Invited
  • [Presentation] On the maximizing problem associated with Trudinger-Moser type inequalities2016

    • Author(s)
      Hidemitsu Wadade
    • Organizer
      Bifurcations and Asymptotic Analysis of Solutions of Nonlinear Models
    • Place of Presentation
      Orlando, Florida, USA
    • Year and Date
      2016-06-01
    • Related Report
      2016 Annual Research Report
    • Int'l Joint Research
  • [Presentation] The Cauchy problem for a semilinear field equation in complex coordinates2016

    • Author(s)
      M. Nakamura
    • Organizer
      Workshop on Mathematical Sciences
    • Place of Presentation
      Wayamba University of Sri Lanka, Sri Lanka.
    • Related Report
      2016 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] On the nonrelativistic limits of semilinear field equations for complex metrics2016

    • Author(s)
      M. Nakamura
    • Organizer
      研究会「Topics on Partial Differential Equations」
    • Place of Presentation
      京都産業大学(京都府)
    • Related Report
      2016 Annual Research Report
  • [Presentation] A criterion for the global boundedness of locally bounded integral operators2016

    • Author(s)
      M.Sugimoto
    • Organizer
      4th East Asian Conference in Harmonic Analysis and Applications
    • Place of Presentation
      韓国・延世大学校
    • Related Report
      2016 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Optimal smoothing estimates and related topics2016

    • Author(s)
      M.Sugimoto
    • Organizer
      Linear and Nonlinear Waves, No.14
    • Place of Presentation
      滋賀県立県民交流センター
    • Related Report
      2016 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Optimal smoothing estimates and a related PDE problem2016

    • Author(s)
      M.Sugimoto
    • Organizer
      Al-Khorezmiy 2016
    • Place of Presentation
      ウズベキスタン・ブハラ州立大
    • Related Report
      2016 Annual Research Report
    • Int'l Joint Research / Invited
  • [Funded Workshop] General Relativity and Partial Differential Equation2019

    • Related Report
      2019 Annual Research Report
  • [Funded Workshop] The 12th International ISAAC Congress2019

    • Related Report
      2019 Annual Research Report
  • [Funded Workshop] Lectures “A novel integral transform approach to PDEs in the curved space-times”2018

    • Related Report
      2018 Annual Research Report
  • [Funded Workshop] Seminar “Analysis on Partial Differential Equations”2018

    • Related Report
      2018 Annual Research Report
  • [Funded Workshop] 研究会“Partial Differential Equation and General Relativity” (Yamagata)2018

    • Related Report
      2018 Annual Research Report
  • [Funded Workshop] 研究会“Partial Differential Equation and General Relativity” (Nagoya)2018

    • Related Report
      2018 Annual Research Report

URL: 

Published: 2016-04-21   Modified: 2024-01-30  

Information User Guide FAQ News Terms of Use Attribution of KAKENHI

Powered by NII kakenhi