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Spacetime estimates for dispersive equations and applications to nonlinear prooblems

Research Project

Project/Area Number 18K03370
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Review Section Basic Section 12020:Mathematical analysis-related
Research InstitutionShimane University

Principal Investigator

Wada Takeshi  島根大学, 学術研究院理工学系, 教授 (70294139)

Co-Investigator(Kenkyū-buntansha) 中村 誠  大阪大学, 大学院情報科学研究科, 教授 (70312634)
北 直泰  熊本大学, 大学院先端科学研究部(工), 教授 (70336056)
Project Period (FY) 2018-04-01 – 2023-03-31
Project Status Completed (Fiscal Year 2022)
Budget Amount *help
¥4,030,000 (Direct Cost: ¥3,100,000、Indirect Cost: ¥930,000)
Fiscal Year 2022: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2021: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2020: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2019: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2018: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Keywords非線形偏微分方程式 / 分散型方程式 / 時空間評価 / Schrodinger 方程式 / 適切性 / 解の時間大域的挙動 / 非線形分散型方程式 / 連立系 / Maxwell 方程式 / 非線形Schrodinger方程式 / 臨界指数 / Benjamin-Ono 方程式 / 解の漸近挙動 / 非線形 Schrodinger 方程式 / 解の時空間評価 / 非線形シュレディンガー方程式 / 平滑化効果 / Strichartz 型評価
Outline of Final Research Achievements

Waves whose phase speed varies with wavelength are said to be dispersive. This study is mainly devoted to the nonlinear Schrodinger equation, which is a typical example of nonlinear dispersive equations, and the Maxwell-Schrodinger system, which is a coupled system of dispersive and hyperbolic equations. We studied the solvability and solution behavior of these equations by functional analytic methods. We proved modifications of Strichartz and Kato type smoothing estimates, which are fundamental tools in the analysis of nonlinear dispersive equations, and improved the results on the solvability of the initial value problem of nonlinear Schrodinger equations. Furthermore, we clarified time global behavior of solutions of the Maxwell-Schrodinger and Benjamin-Ono equations.

Academic Significance and Societal Importance of the Research Achievements

本研究における非線形 Schrodinger 方程式の初期値問題の適切性に関する結果は初期データが小さい場合には最良と考えられるものであり,これによって同方程式の数学的構造が明確になったといえる。

Report

(6 results)
  • 2022 Annual Research Report   Final Research Report ( PDF )
  • 2021 Research-status Report
  • 2020 Research-status Report
  • 2019 Research-status Report
  • 2018 Research-status Report
  • Research Products

    (74 results)

All 2023 2022 2021 2020 2019 2018

All Journal Article (26 results) (of which Int'l Joint Research: 1 results,  Peer Reviewed: 25 results,  Open Access: 4 results) Presentation (46 results) (of which Int'l Joint Research: 18 results,  Invited: 23 results) Book (2 results)

  • [Journal Article] On local well-posedness for Hs-critical nonlinear Schrodinger equations2023

    • Author(s)
      Tabata, Kosuke; Wada, Takeshi
    • Journal Title

      Journal of Evolution Equations

      Volume: 23 Issue: 2

    • DOI

      10.1007/s00028-023-00889-9

    • Related Report
      2022 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Polynomial deceleration for a system of cubic nonlinear Schrodinger equations in one space dimension2023

    • Author(s)
      N.Kita, S.Masaki, J.Segata, K.Uriya
    • Journal Title

      Nonlinear Analysis

      Volume: 230 Pages: 113216-113216

    • DOI

      10.1016/j.na.2023.113216

    • Related Report
      2022 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] Optimal L^2-decay of solutions to the dissipative nonlinear Schrodinger equation in higher space dimensions2023

    • Author(s)
      N.Kita, T.Sato
    • Journal Title

      Journal of Differential Equations

      Volume: 354 Pages: 49-66

    • DOI

      10.1016/j.jde.2023.01.001

    • Related Report
      2022 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] Optimal $$L^2$$-decay of solutions to a nonlinear Schrodinger equation with sub-critical dissipative nonlinearity2022

    • Author(s)
      Kita Naoyasu、Sato Takuya
    • Journal Title

      Nonlinear Differential Equations and Applications NoDEA

      Volume: 29 Issue: 4 Pages: 41-41

    • DOI

      10.1007/s00030-022-00772-5

    • Related Report
      2022 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] Optimal L^2-decay of solutions to a cubic dissipative nonlinear Schrodinger equation2022

    • Author(s)
      Kita, Naoyasu; Sato, Takuya
    • Journal Title

      Asymptotic Analysis

      Volume: 印刷中

    • Related Report
      2021 Research-status Report
    • Peer Reviewed
  • [Journal Article] On the Cauchy problem for the Klein-Gordon equation with the Hartree type semilinear term in the de Sitter spacetime2021

    • Author(s)
      M. Nakamura; H. Takashima
    • Journal Title

      Differential and Integral Equations

      Volume: 34 Pages: 351-382

    • Related Report
      2021 Research-status Report
    • Peer Reviewed
  • [Journal Article] EXISTENCE AND NON-EXISTENCE OF GLOBAL SOLUTIONS FOR THE SEMILINEAR COMPLEX GINZBURG-LANDAU TYPE EQUATION IN HOMOGENEOUS AND ISOTROPIC SPACETIME2021

    • Author(s)
      NAKAMURA Makoto; SATO Yuya
    • Journal Title

      Kyushu Journal of Mathematics

      Volume: 75 Issue: 2 Pages: 169-209

    • DOI

      10.2206/kyushujm.75.169

    • NAID

      130008101303

    • ISSN
      1340-6116, 1883-2032
    • Related Report
      2021 Research-status Report
    • Peer Reviewed
  • [Journal Article] Sharp asymptotic behavior of solutions to Benjamin-Ono type equations---short range case2021

    • Author(s)
      Kita, Naoyasu; Wada, Takeshi
    • Journal Title

      Journal of Mathematical Analysis and Applications

      Volume: 497 Issue: 2 Pages: 124879-124879

    • DOI

      10.1016/j.jmaa.2020.124879

    • Related Report
      2020 Research-status Report
    • Peer Reviewed
  • [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 Research-status 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
      2021 Research-status Report
    • Peer Reviewed
  • [Journal Article] On the nonrelativistic limit of a semilinear field equation in a homogeneous and isotropic space2020

    • Author(s)
      Nakamura, Makoto
    • Journal Title

      Kyoto Journal of Mathematics

      Volume: 60 Issue: 4

    • DOI

      10.1215/21562261-2019-0063

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

    • Author(s)
      Nakamura, Makoto; Sato, Yuya
    • Journal Title

      Hokkaido Mathematical Journal

      Volume: 49 Issue: 3

    • DOI

      10.14492/hokmj/1607936539

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

    • Author(s)
      Nakamura, Makoto
    • Journal Title

      Tsukuba Journal of Mathematics

      Volume: 44 Issue: 2

    • DOI

      10.21099/tkbjm/20204402271

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

    • Author(s)
      Nakamura, Makoto
    • Journal Title

      Advanced Studies in Pure Mathematics

      Volume: 85

    • Related Report
      2020 Research-status Report
    • Peer Reviewed
  • [Journal Article] Long range scattering for the Maxwell-Schrodinger system in the Lorenz gauge without any restriction on the size of data2020

    • Author(s)
      Liu, Yang; Wada, Takeshi
    • Journal Title

      Journal of Differential Equations

      Volume: 269 Issue: 4 Pages: 2798-2852

    • DOI

      10.1016/j.jde.2020.02.013

    • Related Report
      2019 Research-status Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Remarks on the derivation of several second order partial differential equations from a generalization of the Einstein equations2020

    • Author(s)
      Nakamura, Makoto
    • Journal Title

      Osaka Journal of Mathematics

      Volume: 57

    • NAID

      120006846161

    • Related Report
      2019 Research-status Report
    • Peer Reviewed
  • [Journal Article] Strichartz type estimates in mixed Besov spaces with application to critical nonlinear Schrodinger equations2019

    • Author(s)
      Nakamura, Makoto; Wada, Takeshi
    • Journal Title

      Journal of Differential Equations

      Volume: 267 Issue: 5 Pages: 3162-3180

    • DOI

      10.1016/j.jde.2019.04.003

    • Related Report
      2019 Research-status Report
    • Peer Reviewed
  • [Journal Article] Optimal decay rate of solutions to 1D Schrodinger Equation with cubic dissipative nonlinearity2019

    • Author(s)
      Kita, Naoyasu
    • Journal Title

      Journal of Applied Science and Engineering A

      Volume: 1

    • Related Report
      2019 Research-status Report
    • Peer Reviewed
  • [Journal Article] Decay estimate and asymptotic behavior of small solutions to Schrodinger equations with subcritical nonlinearity2019

    • Author(s)
      Kita, Naoyasu; Nakamura, Yoshihisa
    • Journal Title

      Advanced Study of Pure Mathematics

      Volume: 81

    • Related Report
      2019 Research-status Report
    • Peer Reviewed
  • [Journal Article] Large time behavior of small solutions to multi-component nonlinear Schrodinger equations related with spinor Bose-Einstein condensate2019

    • Author(s)
      Kita, Naoyasu; Nakamura, Yoshihisa
    • Journal Title

      Linear and Nonlinear Analysis

      Volume: 5

    • Related Report
      2019 Research-status Report
    • Peer Reviewed
  • [Journal Article] On the numerical experiments of the Cauchy problem for semi-linear Klein-Gordon equations in the de Sitter spacetime2019

    • Author(s)
      Tsuchiya, Takuya; Nakamura, Makoto
    • Journal Title

      Journal of Computational and Applied Mathematics

      Volume: 361 Pages: 396-412

    • DOI

      10.1016/j.cam.2019.05.005

    • Related Report
      2019 Research-status Report
    • Peer Reviewed
  • [Journal Article] On the Regularity of the Semilinear Term on the Cauchy Problem for the Schrodinger Equation2019

    • Author(s)
      Nakamura, Makoto
    • Journal Title

      Trends in Mathematics

      Volume: - Pages: 369-377

    • DOI

      10.1007/978-3-030-04459-6_35

    • ISBN
      9783030044589, 9783030044596
    • Related Report
      2019 Research-status Report
    • Peer Reviewed
  • [Journal Article] A remark on local well-posedness for nonlinear Schrodinger equations with power nonlinearity-an alternative approach2019

    • Author(s)
      Wada, Takeshi
    • Journal Title

      Communications on Pure and Applied Analysis

      Volume: 18 Issue: 3 Pages: 1359-1374

    • DOI

      10.3934/cpaa.2019066

    • Related Report
      2018 Research-status Report
    • Peer Reviewed
  • [Journal Article] Large time behavior of small solutions to multi-component nonlinear Schrodinger equations related with spinor Bose-Einstein condensate2019

    • Author(s)
      Kita, Naoyasu; Nakamura, Yoshihisa
    • Journal Title

      Linear and Nonlinear Analysis

      Volume: 印刷中

    • Related Report
      2018 Research-status Report
    • Peer Reviewed
  • [Journal Article] The Least Number of Intersection Points in Currency Fluctuation and Well- Approximating Line Graph under Constraints of the Elliott Wave Principle2018

    • Author(s)
      Kita, Naoyasu; Matsukuma, Taisei
    • Journal Title

      SCIENCE NATURE

      Volume: 1 Issue: 1 Pages: 033-041

    • DOI

      10.30598/snvol1iss1pp033-041year2018

    • Related Report
      2018 Research-status Report
    • Peer Reviewed / Open Access
  • [Journal Article] On the effects of spatial expansion and contraction on several semilinear partial differential equations2018

    • Author(s)
      Nakamura, Makoto
    • Journal Title

      京都大学数理解析研究所講究録

      Volume: 2093 Pages: 27-37

    • Related Report
      2018 Research-status Report
  • [Presentation] On the Klein-Gordon equation under the quartic potential in the de Sitter spacetime2023

    • Author(s)
      M. Nakamura
    • Organizer
      Japanese Academic Seminars at Stanford (Stanford University)
    • Related Report
      2022 Annual Research Report
    • Int'l Joint Research
  • [Presentation] The Cauchy problem of Klein-Gordon equation under the quartic potential in the de Sitter spacetime2023

    • Author(s)
      M. Nakamura
    • Organizer
      Distinguished Colloquium Series (The University of Texas Rio Grande Valley)
    • Related Report
      2022 Annual Research Report
    • Int'l Joint Research
  • [Presentation] 複素係数をもつ非線形シュレーディンガー方程式の解の挙動2023

    • Author(s)
      北 直泰
    • Organizer
      日本数学会 2023年度年会・函数方程式論分科会
    • Related Report
      2022 Annual Research Report
    • Invited
  • [Presentation] 非線形消散型シュレディンガー方程式の指定されたL2減衰オーダーを もつ解の存在2023

    • Author(s)
      北 直泰
    • Organizer
      反応拡散方程式と非線形分散型方程式の解の挙動
    • Related Report
      2022 Annual Research Report
  • [Presentation] 臨界非線形 Schrodinger 方程式の適切性について2022

    • Author(s)
      和田健志
    • Organizer
      Dispersive and wave equations
    • Related Report
      2022 Annual Research Report
    • Invited
  • [Presentation] Global solutions and blow-up solutions of power-type semilinear Klein-Gordon equations in the de Sitter spacetime2022

    • Author(s)
      M. Nakamura
    • Organizer
      微分方程式セミナー(大阪大学)
    • Related Report
      2022 Annual Research Report
  • [Presentation] The Cauchy problem for the Klein-Gordon equation under the quartic potential in the de Sitter spacetime2022

    • Author(s)
      M. Nakamura
    • Organizer
      応用解析研究会(早稲田大学)
    • Related Report
      2022 Annual Research Report
  • [Presentation] Global solutions for semilinear Proca equations in the de Sitter spacetime2022

    • Author(s)
      M. Nakamura
    • Organizer
      NLPDEセミナー(京都大学)
    • Related Report
      2022 Annual Research Report
  • [Presentation] Global solutions for the Klein-Gordon equation under the quartic potential in the de Sitter spacetime2022

    • Author(s)
      M. Nakamura
    • Organizer
      熊本大学応用解析セミナー
    • Related Report
      2022 Annual Research Report
  • [Presentation] Existence and non-existence of global solutions for the Klein-Gordon equation in the de Sitter spacetime2022

    • Author(s)
      M. Nakamura
    • Organizer
      第65回南大阪応用数学セミナー(大阪公立大学)
    • Related Report
      2022 Annual Research Report
  • [Presentation] Semilinear Proca equations in the de Sitter spacetime2022

    • Author(s)
      M. Nakamura
    • Organizer
      第18回非線型の諸問題(オンライン)
    • Related Report
      2022 Annual Research Report
    • Invited
  • [Presentation] On the Cauchy problem for the Klein-Gordon equation under the quartic potential in the de Sitter spacetime2022

    • Author(s)
      M. Nakamura
    • Organizer
      Analysis & PDE seminar (Stanford University)
    • Related Report
      2022 Annual Research Report
    • Int'l Joint Research
  • [Presentation] L^2-decay rate of solutions to dissipative nonlinear Schrodinger equations2022

    • Author(s)
      N. Kita
    • Organizer
      Mathematical Analysis of Nonlinear Dispersive and Wave Equations
    • Related Report
      2022 Annual Research Report
    • Invited
  • [Presentation] 臨界非線形 Schrodinger 方程式の適切性について2021

    • Author(s)
      和田 健志
    • Organizer
      南大阪応用数学セミナー
    • Related Report
      2021 Research-status Report
  • [Presentation] Existence of blowing-up solution to some Schrodinger equations including nonlinear amplification with small initial data2021

    • Author(s)
      Kita, Naoyasu
    • Organizer
      International Conference on Applied Science and Engineering
    • Related Report
      2021 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] On the Cauchy problem for the semilinear Proca equations in the de Sitter spacetime2021

    • Author(s)
      M. Nakamura
    • Organizer
      The 13th International ISAAC Congress
    • Related Report
      2021 Research-status Report
    • Int'l Joint Research
  • [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 Research-status Report
  • [Presentation] Maxwell-Schrodinger 方程式系の大きなデータに対する長距離型散乱について2020

    • Author(s)
      和田健志
    • Organizer
      第16回非線型の諸問題
    • Related Report
      2020 Research-status Report
    • Invited
  • [Presentation] Maxwell-Schrodinger 方程式の波動作用素の存在について2020

    • Author(s)
      和田健志
    • Organizer
      Critical exponent and nonlinear evolution equations 2020
    • Related Report
      2019 Research-status Report
    • Invited
  • [Presentation] Maxwell-Schrodinger 方程式の散乱理論について2020

    • Author(s)
      和田健志
    • Organizer
      反応拡散方程式と非線形分散型方程式の解の挙動
    • Related Report
      2019 Research-status Report
    • Invited
  • [Presentation] Long Range Scattering for the Maxwell―Schrodinger System2019

    • Author(s)
      和田健志
    • Organizer
      The 17th Linear and Nonlinear Waves
    • Related Report
      2019 Research-status Report
    • Invited
  • [Presentation] Nonlinear Schrodinger equation with delta-functions as initial data (including the case of triple delta-functions)2019

    • Author(s)
      Kita, Naoyasu
    • Organizer
      2019工学ワークショップ
    • Related Report
      2019 Research-status Report
    • Int'l Joint Research
  • [Presentation] Nonlinear Schrodinger equation with delta-functions as initial data2019

    • Author(s)
      Kita, Naoyasu
    • Organizer
      Japan-Mongolia Joint Workshop on Pure and Applied Mathematics
    • Related Report
      2019 Research-status Report
    • Int'l Joint Research
  • [Presentation] Optimal decay rate of global solutions to the Schrodinger equation with cubic dissipative nonlinearity2019

    • Author(s)
      Kita, Naoyasu
    • Organizer
      International seminar "Differential-Algebraic and Integro-Algebraic Systems of Equations : Numerical Methods and Applications to Control Problems"
    • Related Report
      2019 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Decay rate of global solutions to the Schrodinger equation with cubic dissipative nonlinearity2019

    • Author(s)
      Kita, Naoyasu
    • Organizer
      the First International Conference of Applied Sciences and Engineering
    • Related Report
      2019 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] On the Cauchy problem for a semilinear ordinary differential equation in homogeneous and isotropic spaces2019

    • Author(s)
      Nakamura, Makoto
    • Organizer
      日本数学会2019年度秋季総合分科会応用数学分科会
    • Related Report
      2019 Research-status Report
  • [Presentation] On global solutions for the semilinear complex Ginzburg-Landau type equation in homogeneous and isotropic spaces2019

    • Author(s)
      Nakamura, Makoto
    • Organizer
      日本数学会2019年度秋季総合分科会応用数学分科会
    • Related Report
      2019 Research-status Report
  • [Presentation] On the Cauchy problem for the Navier-Stokes equations in the de Sitter spacetime2019

    • Author(s)
      Nakamura, Makoto
    • Organizer
      日本数学会2019年度秋季総合分科会応用数学分科会
    • Related Report
      2019 Research-status Report
  • [Presentation] Partial differential equations in homogeneous and isotropic spaces2019

    • Author(s)
      Nakamura, Makoto
    • Organizer
      日本数学会2019年度秋季総合分科会実関数論分科会
    • Related Report
      2019 Research-status Report
    • Invited
  • [Presentation] On the Cauchy problem for the semilinear Proca equations in the de Sitter spacetime2019

    • Author(s)
      Nakamura, Makoto
    • 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
    • Related Report
      2019 Research-status Report
  • [Presentation] Asymptotic profiles of global solutions for the semilinear diffusion equation in the de Sitter spacetime2019

    • Author(s)
      Nakamura, Makoto; Takeda, H.
    • 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
    • Related Report
      2019 Research-status Report
  • [Presentation] Some dissipative and anti-dissipative effects on semilinear PDEs in homogeneous and isotropic spaces2019

    • Author(s)
      Nakamura, Makoto
    • 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---
    • Related Report
      2019 Research-status Report
    • Invited
  • [Presentation] On the semilinear partial differential equations in homogeneous and isotropic spacetimes2019

    • Author(s)
      Nakamura, Makoto
    • Organizer
      Geometric Analysis and General Relativity
    • Related Report
      2019 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Remarks on the Navier-Stokes equations in homogeneous and isotropic spacetimes2019

    • Author(s)
      Nakamura, Makoto
    • Organizer
      第21回「特異点と時空、および関連する物理」研究会
    • Related Report
      2019 Research-status Report
  • [Presentation] Remarks on a semilinear diffusion equation in homogeneous and isotropic spaces,2019

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

    • Author(s)
      Nakamura, Makoto
    • Organizer
      Nonlinear Dispersive Equations in Kumamoto, 2019
    • Related Report
      2018 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Partial differential equations in uniform and isotropic spaces2019

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

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

    • Author(s)
      Nakamura, Makoto
    • Organizer
      日本数学会年会
    • Related Report
      2018 Research-status Report
  • [Presentation] Strichartz type estimates in mixed Besov spaces with application to critical nonlinear Schrodinger equations2018

    • Author(s)
      和田 健志
    • Organizer
      夏の偏微分方程式セミナー
    • Related Report
      2018 Research-status Report
  • [Presentation] Reduction of nonlinear Schrodinger equations with singular initial data into ODEs2018

    • Author(s)
      Kita, Naoyasu
    • Organizer
      Qualitative Theory on ODEs and their applications to Mathematical Modeling
    • Related Report
      2018 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] On some effects of background metrics for several partial differential equations2018

    • Author(s)
      Nakamura, Makoto
    • Organizer
      The 11th Mathematical Society of Japan, Seasonal Institute (MSJ-SI): The Role of Metrics in the Theory of Partial Differential Equations
    • Related Report
      2018 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] On the dissipative effect of the spatial expansion for the semilinear diffusion equation2018

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

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

    • Author(s)
      Nakamura, Makoto
    • Organizer
      Wayamba International Conference
    • Related Report
      2018 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] The Cauchy problem for Navier-Stokes equations in de Sitter spacetime2018

    • Author(s)
      Nakamura, Makoto; Sato Y.
    • Organizer
      Wayamba International Conference
    • Related Report
      2018 Research-status Report
    • Int'l Joint Research / Invited
  • [Book] 微分積分学入門2022

    • Author(s)
      辻川 亨, 北 直泰
    • Total Pages
      264
    • Publisher
      学術図書出版社
    • Related Report
      2021 Research-status Report
  • [Book] 基礎と応用 微分方程式入門2019

    • Author(s)
      北 直泰、熊本大学工学部機械数理工学科
    • Total Pages
      160
    • Publisher
      学術図書出版社
    • ISBN
      9784780606621
    • Related Report
      2018 Research-status Report

URL: 

Published: 2018-04-23   Modified: 2024-01-30  

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