Mathematical analysis of inverse problems and modelling for complex fluids and diffusion in heterogeneous media

• Project/Area Number: 20H00117
• Research Category: Grant-in-Aid for Scientific Research (A)
• Allocation Type: Single-year Grants
• Section: 一般
• Review Section: Medium-sized Section 12:Analysis, applied mathematics, and related fields
• Research Institution: The University of Tokyo
• Principal Investigator: 山本 昌宏 東京大学, 大学院数理科学研究科, 特任教授 (50182647)
• Co-Investigator(Kenkyū-buntansha): 赤木 剛朗 東北大学, 理学研究科, 教授 (60360202) ; 木村 正人 金沢大学, 数物科学系, 教授 (70263358)
• Project Period (FY): 2020-04-01 – 2025-03-31
• Project Status: Granted (Fiscal Year 2024)
• Budget Amount: ¥39,390,000 (Direct Cost: ¥30,300,000、Indirect Cost: ¥9,090,000); Fiscal Year 2024: ¥7,930,000 (Direct Cost: ¥6,100,000、Indirect Cost: ¥1,830,000); Fiscal Year 2023: ¥7,540,000 (Direct Cost: ¥5,800,000、Indirect Cost: ¥1,740,000); Fiscal Year 2022: ¥7,410,000 (Direct Cost: ¥5,700,000、Indirect Cost: ¥1,710,000); Fiscal Year 2021: ¥7,930,000 (Direct Cost: ¥6,100,000、Indirect Cost: ¥1,830,000); Fiscal Year 2020: ¥8,580,000 (Direct Cost: ¥6,600,000、Indirect Cost: ¥1,980,000)
• Keywords: 逆問題 / 複雑流体 / 特異拡散 / 定性理論 / 非線形理論 / 非整数階偏微分方程式 / 安定性 / 一意性 / 数値手法 / カーレマン評価 / 非整数階拡散方程式 / 粘弾性 / 順問題理論

Outline of Research at the Start

応用上重要である固体と液体が絡む複雑流体や不均質媒質中の拡散現象の順問題と逆問題の数学解析、ならびに応用を視野にいれた数値解析手法の開発を目指す。逆問題は、観測データの適切な解釈と汚染などの精密な予測のための支配方程式のモデリングに本質的に関わる。一方で順問題は支配方程式が数学的に意味を持つかに関する基本的な課題である。主な対象は複雑流体の方程式と非整数階偏微分方程式であり、それらの方程式の逆問題の理論の構築を第一の目標とする。逆問題の前提となる非整数階偏微分方程式の解の一意存在などの順問題の包括的な理論体系の構築が第二目標である。第三の目標は現場に密着した数値解析を目指すことである。

Outline of Annual Research Achievements

１．カーレマン評価は偏微分方程式の一般論展開のために研究されてきたが、逆問題への応用に関しては従来の理論では、偏微分方程式の主要部などに依存する条件の検証がしばしば困難で、係数決定逆問題の応用のために有効ではなかった。またその導出も過度に一般論に依存しており、応用分野での認知度は低い状態であり、広範な共同研究を妨げ、本来であれば応用分野も巻き込んだ逆問題の数学研究のコアになっていなかった。そこで、カーレマン評価自体を根本から見直し、逆問題への応用を見据えた直接的な導出などを確立した。これは単行本として出版準備中であり、本研究計画の主要テーマの１つである複雑流体の逆問題への効率的な応用が可能となる素地ができた。　２．非整数階偏微分方程式の初期値・境界値問題の数学理論を確立した。解のクラスを弱解、強解のクラスなどを確立したうえで、解の一意存在、漸近挙動などを厳密な理論の枠内で示した。　３．２の成果も活用して、係数決定、ソース項決定、階数などの物理パラメータ決定の逆問題の数学解析を実施し、成果をあげた。４．関連する非線形非整数階偏微分方程式の定性理論や数値手法の研究を行った。

Current Status of Research Progress

2: Research has progressed on the whole more than it was originally planned.

Reason

１．カーレマン評価による逆問題の手法を確立し、本研究計画の主要テーマの複雑流体だけでなく数理物理に現れる偏微分方程式に広
く適用できるようになったこと。２．カーレマン評価による逆問題の手法の研究に付随して、それが成立するための偏微分方程式の主要部の条件をより実用的な
背景の下に明らかにしたこと。これは方程式の特性を検知できないことがあるような領域を明らかにすることにもつながり、逆問題の研究に新たな視野を開きう
ると期待できること。３．非整数階偏微分方程式の作用素論からの線形理論をほぼ完了させ、非線形問題や逆問題の数学解析を順調に進めていること。４．非整
数階拡散・波動方程式の様々な逆問題の数学解析について、国際的な共同研究も組織して、世界の研究動向をリードする成果をあげつつあること。

Strategy for Future Research Activity

課題の観点からは以下を目指す。（１）線形の場合の非整数階偏微分方程式論はほぼ完了したので、それを受けて非線形理論の確立を目指す。（２）複雑流体の
逆問題については確立した方法論を、対象となってる多様な流体の方程式に応じて、適宜修正して応用し安定性、一意性を確立していく。
実施の形態は前年度と同様であり、海外の連携研究者などとの共同研究や本課題による研究の国際的な周知と優先権の確立を期すための海外での研究連絡を計画
している。

Research Products

• [Int'l Joint Research] Fudan University/Ninpo Univ.(中国)
• [Int'l Joint Research] Colorado State University/Texas A&M University(米国)
• [Int'l Joint Research] Beuth Tech. Hochschule(ドイツ)
• [Int'l Joint Research] Sapienza University of Rome(イタリア)
• [Int'l Joint Research] Aix-Marseille University(フランス)
• [Int'l Joint Research]
• [Int'l Joint Research] Colorado State Univ.(米国)
• [Int'l Joint Research] Fudan Univ./Changan Univ. Xian(中国)
• [Int'l Joint Research] Sapienza Univ. Rome/Univ. Rome Tor Vergata/Univ. Pisa(イタリア)
• [Int'l Joint Research] Beuth Tech. Hochschule(ドイツ)
• [Int'l Joint Research] Univ. Sevilla(スペイン)
• [Int'l Joint Research]
• [Int'l Joint Research] Fudan University/Nanhai Math. Institute(中国)
• [Int'l Joint Research] Aix Marseille University(フランス)
• [Int'l Joint Research] Beuth Tech. Hochschule(ドイツ)
• [Int'l Joint Research] University of Klagenfurt(オーストリア)
• [Int'l Joint Research] Sapienza University of Rome/University of Bari(イタリア)
• [Int'l Joint Research]
• [Int'l Joint Research] Weiertrass Institute/Beuth Tech. Hochschule(ドイツ)
• [Int'l Joint Research] Aix Marseille Univ.(フランス)
• [Int'l Joint Research] Fudan Univ./Chinese Academy of Natural Sciences(中国)
• [Int'l Joint Research] Academy of Romanian Scientists(ルーマニア)
• [Int'l Joint Research] Sapienza University of Rome/University of Napoli Federico II(イタリア)
• [Int'l Joint Research]
• [Journal Article] Inverse source problem for a one-dimensional time-fractional diffusion equation and unique continuation for weak solutions (2023)
  • Author(s): Z. Li, Y.Liu and M. Yamamoto
  • Journal Title: Inverse Prob. Imaging Volume: 17 Pages: 1-22
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] Uniqueness of orders and parameters in multi-term time-fractional diffusion equations by short-time behavior (2023)
  • Author(s): Y. Liu, and M. Yamamoto
  • Journal Title: Inverse Prob. Volume: 39 Pages: 024003-28
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] Uniqueness for fractional nonsymmetric diffusion equations and an application to an inverse source problem (2023)
  • Author(s): D. Jiang, Z. Li, M. Pauron, M. Yamamoto
  • Journal Title: Math. Methods Appl. Sci. Volume: 46 Pages: 2275-2287
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] Uniqueness for inverse source problems for fractional diffusion-wave equations by data during not acting time (2023)
  • Author(s): M. Yamamoto
  • Journal Title: Inverse Prob. Volume: 39 Pages: 024004-20
  • Peer Reviewed
• [Journal Article] Carleman estimates for a magnetohydrodynamics system and application to inverse source problems (2023)
  • Author(s): X. Huang, M. Yamamoto
  • Journal Title: Math. Control Relat. Fields Volume: 13 Pages: 470-499
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] Uniqueness for inverse problem of determining fractional orders for time-fractional advection-diffusion equations (2023)
  • Author(s): M. Yamamoto
  • Journal Title: Math. Control Relat. Fields Volume: 13 Pages: 833-851
  • Peer Reviewed
• [Journal Article] Determination of source terms in diffusion and wave equations by observations after incidents: uniqueness and stability (2023)
  • Author(s): J. Cheng, S. Lu and M. Yamamoto
  • Journal Title: CSIAM Trans. Appl. Math. Volume: 4 Pages: 381-418
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] Uniqueness for an inverse coefficient problem for a one-dimensional time-fractional diffusion equation with non-zero boundary conditions (2023)
  • Author(s): W. Rundell and M. Yamamoto
  • Journal Title: Appl. Anal. Volume: 102 Pages: 815-829
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] Global Lipschitz stability for an inverse source problem for the Navier-Stokes equations (2023)
  • Author(s): O. Imanuvilov and M. Yamamoto
  • Journal Title: Appl. Anal. Volume: 102 Pages: 2200-2210
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] Uniqueness of inverse source problems for general evolution equations (2023)
  • Author(s): Y. Kian, Y. Liu and M. Yamamoto
  • Journal Title: Commun. Contemp. Math. Volume: 25 Pages: 2250009-33
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] Unique continuation for a mean field game system (2023)
  • Author(s): O. Imanuvilov, H. Liu and M. Yamamoto
  • Journal Title: Appl. Math. Lett. Volume: 145 Pages: 108757-6
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] Comparison principles for the time-fractional diffusion equations with the Robin boundary conditions. Part I: Linear equations (2023)
  • Author(s): Y. Luchko and M. Yamamoto
  • Journal Title: Fract. Calc. Appl. Anal. Volume: 26 Pages: 1504-1544
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] Determination of source or initial values for acoustic equations with a time-fractional attenuation (2023)
  • Author(s): X. Huang, Y. Kian, E. Soccorsi and M. Yamamoto
  • Journal Title: Anal. Appl. Volume: 21 Pages: 1105-1130
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] Sharp uniqueness and stability of solution for an inverse source problem for the Schrodinger equation (2023)
  • Author(s): O. Imanuvilov and M. Yamamoto
  • Journal Title: Inverse Prob. Volume: 39 Pages: 105013-19
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] Harmonic measures and numerical computation of Cauchy problems for Laplace equations (2023)
  • Author(s): Y. Chen, J. Cheng, S. Lu and M. Yamamoto
  • Journal Title: Chinese Ann. Math. Ser. B Volume: 44 Pages: 913-928
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] Blowup in L^1(Omega)-norm and global existence for time-fractional diffusion equations with polynomial semilinear terms (2023)
  • Author(s): G. Floridia, Y. Liu and M. Yamamoto
  • Journal Title: Adv. Nonlinear Anal. Volume: 12 Pages: 20230121-15
  • Peer Reviewed / Open Access / Int'l Joint Research
• [Journal Article] Homogenization and inverse problems for fractional diffusion equations (2023)
  • Author(s): A. Kawamoto, M. Machida and M. Yamamoto
  • Journal Title: Fract. Calc. Appl. Anal. Volume: 26 Pages: 2118-2165
  • Peer Reviewed
• [Journal Article] On the maximum principle for the multi-term fractional transport equation (2022)
  • Author(s): Luchko, Yuri; Suzuki, Anna; Yamamoto, Masahiro
  • Journal Title: J.Math. Anal. Appl. Volume: 505 Pages: 125579-12
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] Some inverse problems for the Burgers equation and related systems (2022)
  • Author(s): Apraiz, J.; Doubova, A.; Fern\'andez-Cara, E.; Yamamoto, M.
  • Journal Title: ommun. Nonlinear Sci. Numer. Simul. Volume: 107 Pages: 106113-23
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] Identification of time-varying source term in time-fractional evolution equations (2022)
  • Author(s): Kian, Yavar; Soccorsi, Eric; Xue, Qi; Yamamoto, Masahiro
  • Journal Title: Commun. Math. Sci. Volume: 20 Pages: 53-84
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] Inverse parabolic problems of determining functions with one spatial-component independence by Carleman estimate (2022)
  • Author(s): Imanuvilov, Oleg Y.; Kian, Yavar; Yamamoto, Masahiro
  • Journal Title: J. Ill-posed Prob. Volume: 30 Pages: 191-203
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] Uniqueness and numerical reconstruction for inverse problems dealing with interval size search (2022)
  • Author(s): Apraiz, Jone; Cheng, Jin; Doubova, Anna; Fern\'ndez-Cara, Enrique; Yamamoto, Masahiro
  • Journal Title: Inverse Prob. Imaging Volume: 16 Pages: 569-594
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] Continuation of solutions to elliptic and parabolic equations on hyperplanes and application to inverse source problems (2022)
  • Author(s): Cheng, Jin, Yamamoto, Masahiro
  • Journal Title: Inverse Prob. Volume: 38 Pages: 085005-23
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] Carleman estimate for the Navier-Stokes equations and applications (2022)
  • Author(s): O.Y. Imanuvilov, L. Lorenzi and M. Yamamoto
  • Journal Title: Inverse Prob. Volume: 38 Pages: 085006-30
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] A Carleman estimate and an energy method for a first-order symmetric hyperbolic system (2022)
  • Author(s): G. Floridia, H. Takase, M. Yamamoto
  • Journal Title: Inverse Prob. Imaging Volume: 16 Pages: 1163-1178
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] Simultaneous uniqueness for multiple parameters identification in a fractional diffusion-wave equation (2022)
  • Author(s): X. Jing and M. Yamamoto
  • Journal Title: Inverse Prob. Imaging Volume: 16 Pages: 1199-1217
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] Least squares formulation for ill-posed inverse problems and applications (2022)
  • Author(s): E. Chung, K. Ito and M. Yamamoto
  • Journal Title: Appl. Anal. Volume: 101 Pages: 5247-5261
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] Fractional calculus and time-fractional differential equations: revisit and construction of a theory (2022)
  • Author(s): M. Yamamoto
  • Journal Title: Mathematics Volume: special issue Pages: 2227-698
  • Peer Reviewed / Open Access / Int'l Joint Research
• [Journal Article] On time fractional derivatives in fractional Sobolev spaces and applications to fractional ordinary differential equations (2021)
  • Author(s): M. Yamamoto
  • Journal Title: Nonlocal and Fractional Operators, SEMA SIMAI Springer Ser., Springer, Cham Volume: 26 Pages: 287308-287308
  • Peer Reviewed
• [Journal Article] Inverse moving source problem for time-fractional evolution equations: determination of profiles (2021)
  • Author(s): Y. Liu, G. Hui, M. Yamamoto
  • Journal Title: Inverse Problems Volume: 37 Pages: 084001-24
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] Well-posedness for weak and strong solutions of non-homogeneous initial boundary value problems for fractional diffusion equations (2021)
  • Author(s): Y. Kian, M. Yamamoto
  • Journal Title: Fract. Calc. Appl. Anal. Volume: 24 Pages: 168-201
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] The general fractional derivative and related fractional differential equation (2021)
  • Author(s): Y. Luchko, M. Yamamoto
  • Journal Title: Special Issue of ”Mathematics (ISSN 2227-7390)”: ”Fractional Integrals and Derivatives: ”True” versus ”False””, ed: Luchko, Y., Volume: special issue Pages: 120-120
  • Peer Reviewed / Open Access / Int'l Joint Research
• [Journal Article] An inverse source problem related to acoustic nonlinearity parameter (2021)
  • Author(s): M. Yamamoto, B. Kaltenbacher
  • Journal Title: ”Time-dependent Problems in Imaging and Parameter Identification”. eds: Kaltenbacher, B., Schuster, T. and Wald, A. Springer Volume: special issue Pages: 1-45
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] Inverse problem of reconstruction of degenerate diffusion coefficient in a parabolic equation (2021)
  • Author(s): P. Cannarsa, A. Doubova, M. Yamamoto
  • Journal Title: Inverse Problems Volume: 37 Pages: 125002-56
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] Global stability result for parabolic Cauchy problems (2021)
  • Author(s): M. Choulli, M. Yamamoto
  • Journal Title: J. Inverse and Ill-posed Problems Volume: 29 Pages: 895915-895915
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] Conditional stability for an inverse coefficient problem of a weakly coupled time-fractional diffusion system with half order by Carleman estimate (2021)
  • Author(s): C. Ren, X. Huang, M. Yamamoto
  • Journal Title: J. Inverse and Ill-posed Problems Volume: 29 Pages: 635651-635651
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] Uniqueness in determining fractional orders of derivatives and initial values (2021)
  • Author(s): M. Yamamoto
  • Journal Title: Inverse Problems Volume: 37 Pages: 09500634-09500634
  • Peer Reviewed
• [Journal Article] The uniqueness of inverse problems for a fractional equation with a single measurement (2021)
  • Author(s): Y. Kian, Z. Li, Y. Liu, M. Yamamoto
  • Journal Title: Math. Ann. Volume: 380 Pages: 14651495-14651495
  • NAID: 120007116481
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] Carleman estimates and controllability for a degenerate structured population model (2021)
  • Author(s): G. Fragnelli, M. Yamamoto
  • Journal Title: Appl. Math. Optim. Volume: 84 Pages: 999-1044
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] Recovering the weight function in distributed order fractional equation from interior measurement (2021)
  • Author(s): J.J. Liu, C.L. Sun, M. Yamamoto
  • Journal Title: Appl. Numer. Math. Volume: 168 Pages: 84-103
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] Stability estimate for a semilinear elliptic inverse problem (2021)
  • Author(s): M. Choulli, G. Hui, M. Yamamoto
  • Journal Title: NoDEA Nonlinear Differential Equations Appl. Volume: 28 Pages: 37-26
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] Backward problems in time for fractional diffusion-wave equation (2020)
  • Author(s): G. Floridia, M. Yamamoto
  • Journal Title: Inverse Problems Volume: 36 Pages: 125016-14
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] Stability for inverse source problems by Carleman estimates (2020)
  • Author(s): X. Huang, O.Y. Imanuvilov, M. Yamamoto
  • Journal Title: Inverse Problems Volume: 36 Pages: 125006-20
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] A parabolic shape optimization problem (2020)
  • Author(s): D. Tiba, M. Yamamoto
  • Journal Title: Ann. Acad. Rom. Sci. Ser. Math. Appl. Volume: 12 Pages: 313328-313328
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] Well-posedness for the backward problems in time for general time-fractional diffusion equation (2020)
  • Author(s): G. Floridia, Z. Li, M. Yamamoto
  • Journal Title: Atti Accad. Naz. Lincei Rend. Lincei Mat. Appl. Volume: 31 Pages: 593610-593610
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] A Carleman estimate for the linear magnetoelastic waves system and an inverse source problem in a bounded conductive medium (2020)
  • Author(s): M. Bellassoued, M. Chaima, M. Yamamoto
  • Journal Title: Appl. Anal. Volume: 99 Pages: 24282456-24282456
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] Conditional stability for an inverse source problem and an application to the estimation of air dose rate of radioactive substances by drone data (2020)
  • Author(s): Y. Chen, J. Cheng, G. Floridia, Y. Wada, M. Yamamoto
  • Journal Title: Math.Eng. Volume: 2 Pages: 2633-2633
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] A stability result for the determination of order in time-fractional diffusion equations. (2020)
  • Author(s): Z. Li, X. Huang, M. Yamamoto
  • Journal Title: J. Inverse and Ill-posed Problems Volume: 28 Pages: 379386-379386
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] Single logarithmic conditional stability in determining unknown boundaries (2020)
  • Author(s): J. Elschner, G. Hu, M. Yamamoto
  • Journal Title: Appl. Anal. Volume: 99 Pages: 725746-725746
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] Uniqueness of solution of an inverse source problem for ultrahyperbolic equations (2020)
  • Author(s): F. Goelgeleyen, M. Yamamoto
  • Journal Title: Inverse Problems Volume: 36 Pages: 03500817-03500817
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] Carleman estimate for linear viscoelasticity equations and an inverse source problem (2020)
  • Author(s): O.Y. Imanuvilov, M. Yamamoto
  • Journal Title: SIAM J. Math. Anal. Volume: 52 Pages: 718791-718791
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] Unique continuation property with partial information for two-dimensional anisotropic elasticity systems (2020)
  • Author(s): J. Cheng, Y. Liu, Y. Wang, M. Yamamoto
  • Journal Title: Acta Math. Appl. Sin. Engl. Ser. Volume: 36 Pages: 317-317
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] Initial-boundary value problems for multi-term time-fractional diffusion equations with x -dependent coefficients (2020)
  • Author(s): Z. Li, X. Huang, M. Yamamoto
  • Journal Title: Evol. Equ. Control Theory Volume: 9 Pages: 153179-153179
  • Peer Reviewed / Int'l Joint Research
• [Presentation] Stability and uniqueness for inverse problems for partial differential equations by Carleman estimates (2023)
  • Author(s): M. Yamamoto
  • Organizer: 6th Young Scholar Symposium East Asia Section of Inverse Problems International Association
  • Int'l Joint Research / Invited
• [Presentation] Fractional calculus and time-fractional differential equations:revisit and construction of a theory (2022)
  • Author(s): M. Yamamoto
  • Organizer: Differential Equations and their Applications, V. I. Romanovskiy Institute of Mathematics, Uzbekistan Tashkent
  • Int'l Joint Research / Invited
• [Presentation] General treatments for time-fractional diffusion equations and comparison principles (2022)
  • Author(s): M. Yamamoto
  • Organizer: Taishan Science and Technology Forum International Conference on Theory and Computation of Partial Differential Equations
  • Int'l Joint Research / Invited
• [Presentation] Mathematics as foundation for social cooperation; case studies from steel industry to environmental issue (2022)
  • Author(s): M. Yamamoto
  • Organizer: Classe di Scienze Fisiche, Matematiche e Naturali Messina, Italy
  • Invited
• [Presentation] Carleman estimates and inverse problems for transport equation (2021)
  • Author(s): M. Yamamoto
  • Organizer: Analysis and Numerics of Design, Control and Inverse Problems, INdAM Roma
  • Int'l Joint Research / Invited
• [Presentation] Direct and inverse problems for time-fractional partial differential equations (2021)
  • Author(s): M. Yamamoto
  • Organizer: Nonlinear Theory, Analysis, Control, and Numerics for PDE Models of Interest to Physics and Life Sciences, Centro Internazionale per la Ricerca Matematica Trento
  • Int'l Joint Research / Invited
• [Presentation] Inverse problems for transport equations of first order by Carleman estimate (2021)
  • Author(s): M. Yamamoto
  • Organizer: Eurasian Conference on Applied Mathematics, Novosibirsk
  • Int'l Joint Research / Invited
• [Presentation] Some inverse problems for time-fractional diffusion equations (2020)
  • Author(s): M. Yamamoto
  • Organizer: Internationa Workshop on Fractional Calculus, Ghent Analysis & PDE Center, Ghent
  • Int'l Joint Research / Invited
• [Presentation] On an initial boundary value problem for generalized time-fractional partial differential equations: one unified approach (2020)
  • Author(s): M. Yamamoto
  • Organizer: ”Recent Progress in Nonlocal Modeling, Analysis, and Computation ”Southern University of Science and Technology, Shenzheng
  • Int'l Joint Research / Invited
• [Presentation] Unique existence of solutions for some time fractional partial differential equations and some inverse problems: recent results (2020)
  • Author(s): M. Yamamoto
  • Organizer: "Nonlocal Diffusion Problems, Nonlocal Interface Evolution Institute of Mathematics”, Polish Academy of Sciences
  • Int'l Joint Research / Invited
• [Presentation] The theory of the direct problem and several inverse problems for time-fractional partial differential equations (2020)
  • Author(s): M. Yamamoto
  • Organizer: “Inverse and Ill-posed Problems: Theory and Numerics XII International Scientific Conference and Young Scientist School”, Novosibirsk State University, Mathetmaical Center in Akademgorodok
  • Int'l Joint Research / Invited
• [Presentation] モデル駆動型アプローチからみた逆問題の 諸相 (2020)
  • Author(s): M. Yamamoto
  • Organizer: “JST 俯瞰セミナーシリーズ「機械学 習と科学」”
  • Invited
• [Book] Time-fractional differential equationsa theoretical introduction (2020)
  • Author(s): Kubica, Adam; Ryszewska, Katarzyna; Yamamoto, Masahiro
  • Total Pages: 134
  • Publisher: Springer
  • ISBN: 9789811590658