Kazuhiro Takimoto

Last Updated :2024/10/02

Affiliations, Positions
Graduate School of Advanced Science and Engineering, Associate Professor
Web Site
http://www.math.sci.hiroshima-u.ac.jp/~takimoto/index.html
E-mail
ktakimotohiroshima-u.ac.jp
Other Contact Details
"1-3-1 KAGAMIYAMA, HIGASHI-HIROSHIMA CITY, HIROSHIMA", Japan
TEL : (+81)82-424-7332 FAX : (+81)
Self-introduction
Name : Kazuhiro TAKIMOTO Affiliation : Mathematics Program, Division of Advanced Science and Engineering, Graduate School of Advanced Science and Engineering, Hiroshima University (School : Department of Mathematics, School of Science, Hiroshima University) Research field : Nonlinear elliptic and parabolic partial differential equations (Especially, Fully nonlinear partial differential equations such as Hessian equation and curvature equation)

Basic Information

Major Professional Backgrounds

  • 2003/04/01, 2007/03/31, Hiroshima University, Department of Mathematics, Graduate School of Science, Research Associate
  • 2007/04/01, 2008/04/30, Hiroshima University, Department of Mathematics, Graduate School of Science, Assistant Professor
  • 2008/05/01, 2020/03/31, Hiroshima University, Department of Mathematics, Graduate School of Science, Associate Professor
  • 2020/04/01, Hiroshima University, Graduate School of Advanced Science and Engineering, Associate Professor

Educational Backgrounds

  • The University of Tokyo, Graduate School of Mathematical Sciences, Mathematical Sciences, Japan, 1999/04, 2003/03
  • The University of Tokyo, Graduate School of Mathematical Sciences, Mathematical Sciences, Japan, 1997/04, 1999/03
  • The University of Tokyo, Faculty of Science, Department of Mathematics, Japan, 1993/04, 1997/03

Academic Degrees

  • Ph.D. (Mathematical Sciences), The University of Tokyo
  • M.A.(Mathematical Sciences), The University of Tokyo
  • B.A. (Science), The University of Tokyo

Educational Activity

  • [Bachelor Degree Program] School of Science : Mathematics : Mathematics
  • [Master's Program] Graduate School of Advanced Science and Engineering : Division of Advanced Science and Engineering : Mathematics Program
  • [Doctoral Program] Graduate School of Advanced Science and Engineering : Division of Advanced Science and Engineering : Mathematics Program

In Charge of Primary Major Programs

  • Mathematics

Research Fields

  • Mathematical and physical sciences;Mathematics;Mathematical analysis

Research Keywords

  • Fully nonlinear PDE
  • viscosity solutions

Affiliated Academic Societies

  • The Japan Society for Industrial and Applied Mathematics, 2011
  • Mathematical Society of Japan, 2002

Educational Activity

Course in Charge

  1. 2024, Liberal Arts Education Program1, 1Term, Introductory Seminar for First-Year Students
  2. 2024, Undergraduate Education, 2Term, Analysis I
  3. 2024, Undergraduate Education, 2Term, Exercises in Analysis I
  4. 2024, Undergraduate Education, 1Term, Mathematical Analysis A
  5. 2024, Undergraduate Education, First Semester, Special Study of Mathematics and Informatics for Graduation
  6. 2024, Undergraduate Education, Second Semester, Special Study of Mathematics and Informatics for Graduation
  7. 2024, Graduate Education (Master's Program) , 2Term, Mathematical Omnibus
  8. 2024, Graduate Education (Master's Program) , Academic Year, Seminar on Real Analysis and Functional Equations
  9. 2024, Graduate Education (Master's Program) , 1Term, Mathematical Analysis A
  10. 2024, Graduate Education (Master's Program) , 2Term, Mathematical Analysis B
  11. 2024, Graduate Education (Master's Program) , 4Term, Topics in Mathematical Analysis C
  12. 2024, Graduate Education (Master's Program) , 3Term, Topics in Mathematical Analysis D
  13. 2024, Graduate Education (Master's Program) , Academic Year, Exercises in Mathematics
  14. 2024, Graduate Education (Master's Program) , First Semester, Exercises in Mathematics A
  15. 2024, Graduate Education (Master's Program) , Second Semester, Exercises in Mathematics B
  16. 2024, Graduate Education (Master's Program) , Academic Year, Seminar in Mathematics
  17. 2024, Graduate Education (Doctoral Program) , Academic Year, Seminar in Mathematics

Research Activities

Academic Papers

  1. Isolated singularities for some types of curvature equations, Viscosity Solutions of Differential Equations and Related Topics, RIMS Kokyuroku, 1323, 105-123, 20030501
  2. Isolated singularities for some types of curvature equations, Journal of Differential Equations, 197(2), 275-292, 20040301
    Link to Paper Search Results by DOI
  3. Removable singularities for solutions to k-curvature equations, Variational Problems and Related Topics, RIMS Kokyuroku, 1405, 117-130, 20041101
  4. Singular sets for curvature equations of order k, Viscosity Solution Theory of Differential Equations and its Developments, 1428, 91-105, 20050401
  5. Boundary blowup solutions to curvature equations, Proceedings of the 30th Sapporo Symposium on Partial Differential Equations, Hokkaido University Technical Report Series in Mathematics, 96, 18-25, 20050701
  6. Singular sets for curvature equation of order k, Journal of Mathematical Analysis and Applications, 309(1), 227-237, 20050901
    Link to Paper Search Results by DOI
  7. Solutions with boundary blowup for k-curvature equation, Mechanism of temporal and spatial patterns in reation-diffusion systems, RIMS Kokyuroku, 1498, 99-112, 20060601
  8. Solution to the boundary blowup problem for k-curvature equation, Calculus of Variations and Partial Differential Equations, 26(3), 357-377, 20060701
    Link to Paper Search Results by DOI
  9. On the removability of a level set for solutions to fully nonlinear equations, Viscosity Solution Theory of Differential Equations and its Developments, 1545, 13-31, 20070401
  10. Rado type removability result for fully nonlinear equations, Differential and Integral Equations, 20(8), 939-960, 20070801
  11. Generalized solutions of curvature equations, Nonlinear Analysis - Theory, Methods & Applications, 67(4), 1275-1287, 20070815
    Link to Paper Search Results by DOI
  12. Rado type removability result for fully nonlinear PDEs, Proceedings of International Conference for the 25th Anniversary of Viscosity Solutions, 30, 231-241, 20080801
  13. A quasilinear parabolic perturbation of the linear heat equation, Journal of Differential Equations, 252(1), 323-343, 20120101
    Link to Paper Search Results by DOI
  14. A weighted quasilinear equation related to the mean curvature operator, Nonlinear Analysis - Theory, Methods & Applications, 75(15), 5905-5923, 20121001
    Link to Paper Search Results by DOI
  15. Uniqueness of boundary blowup solutions to k-curvature equation, Journal of Mathematical Analysis and Applications Journal of Mathematical Analysis and Applications Journal of Mathematical Analysis and Applications, 399(2), 496-504, 20130315
    Link to Paper Search Results by DOI
  16. A Bernstein type theorem for parabolic k-Hessian equations, Nonlinear Analysis - Theory, Methods & Applications, 117, 211-220, 20150415
    Link to Paper Search Results by DOI
  17. Entire solutions to generalized parabolic k-Hessian equations, Geometric Properties for Parabolic and Elliptic PDE's, Springer Proceedings in Mathematics & Statistics, 176, 173-190, 20160801
    Link to Paper Search Results by DOI
  18. Kral type removability results for k-Hessian equation and k-curvature equation, Differential and Integral Equations, 32(3-4), 211-222, 20190301
  19. Precise blowup rate near the boundary of boundary blowup solutions to k-Hessian equation, SN Partial Differential Equations and Applications, 2(1), 1-10, 20210201
    Link to Paper Search Results by DOI
  20. Bernstein type theorem for the generalized parabolic 2-Hessian equation under weaker conditions, Journal of Mathematical Analysis and Applications, 495(1), 1-14, 20210301
    Link to Paper Search Results by DOI
  21. Second order boundary estimate of boundary blowup solutions to k-Hessian equation, Journal of Mathematical Analysis and Applications, 500(2), 1-12, 20210815
    Link to Paper Search Results by DOI
  22. Exact principal blowup rate near the boundary of boundary blowup solutions to k-curvature equation, Manuscripta Mathematica, 168(3-4), 351-369, 20220701
    Link to Paper Search Results by DOI
  23. The exterior Dirichlet problem for the generalized parabolic k-Hessian equations, Geometric Aspects on Partial Differential Equations, RIMS Kokyuroku, 2251, 29-42, 20230501
  24. Higher order estimate near the boundary of a large solution to semilinear Poisson equation with double-power like nonlinearity, Journal of Mathematical Analysis and Applications, 527(1), 1-13, 20231101
    Link to Paper Search Results by DOI
  25. Asymptotic behavior near the boundary of a large solution to semilinear Poisson equation with double-power nonlinearity, Acta Mathematica Scientia, 44(6), 2083-2098, 20241101
    Link to Paper Search Results by DOI

Publications such as books

  1. 2014/11/01, Mathematical Analysis of Pattern Formation Arising in Nonlinear Phenomena, Research Institute for Mathematical Sciences, Kyoto University, Cocompilation

Invited Lecture, Oral Presentation, Poster Presentation

  1. The dynamics of a quasilinear equation related to the mean curvature operator, Kazuhiro Takimoto, PDE Seminar, 2012/07, With Invitation, Japanese, Hokkaido University
  2. The dynamics of a parabolic quasilinear equation associated to the mean curvature operator, Kazuhiro Takimoto, Nonlinear PDE Workshop at Tohoku University, 2012/09, With Invitation, Japanese, Tohoku University
  3. A quasilinear parabolic perturbation of the linear heat equation, Kazuhiro Takimoto, Colloquium in Ehime University, 2012/10, With Invitation, English, Ehime University
  4. The existence and uniqueness of boundary blowup solutions to $k$-curvature equation, Kazuhiro Takimoto, Seminar in Tokyo University of Science, 2013/01, With Invitation, Japanese, Tokyo University of Science
  5. A quasilinear parabolic perturbation of the linear heat equation, Kazuhiro Takimoto, Applied Analysis Seminar, 2013/01, With Invitation, Japanese, Kumamoto University
  6. The dynamics of a parabolic quasilinear boundary value problem associated to the mean curvature operator, Kazuhiro Takimoto, 3rd Italian-Japanese Workshop on Geometric Properties for Parabolic and Elliptic PDE's, 2013/09/05, With Invitation, English, Tokyo Instuitute of Technology
  7. On the dynamics of a quasilinear parabolic problem related to the mean curvature operator, Kazuhiro Takimoto, San-Daigaku Henbibun Houteishiki Seminar, 2013/11/27, With Invitation, Japanese, Nihon University
  8. Bernstein type theorem for some fully nonlinear PDEs, Kazuhiro Takimoto, 10th AIMS International Conference on Dynamical Systems, Differential Equations and Applications, 2014/07/07, With Invitation, English, Universidad Autónoma de Madrid
  9. Entire solution to the parabolic $k$-Hessian equation, Kazuhiro Takimoto, Gifu Mathematical Science Seminar, 2014/10/24, With Invitation, Japanese, Gifu University
  10. Bernstein type theorem for some parabolic Hessian equation, Kazuhiro Takimoto, Nonlinear PDE Workshop at Tohoku University, 2014/11/15, With Invitation, English, Tohoku University
  11. Entire solution to the parabolic $k$-Hessian equation, Kazuhiro Takimoto, Minami-Osaka Applied Analysis Seminar, 2015/01/31, With Invitation, Japanese, Osaka City University
  12. Bernstein type theorem for the parabolic $k$-Hessian equation, Saori Nakamori, Kazuhiro Takimoto, MSJ Spring Meeting 2015, 2015/03/22, Without Invitation, Japanese, Meiji University
  13. Entire solution to the generalized parabolic $k$-Hessian equation, Kazuhiro Takimoto, Geometric Properties for Parabolic and Elliptic PDE's，4th Italian-Japanese Workshop, 2015/05/27, With Invitation, English, Grand Hotel San Pietro，Palinuro
  14. Entire solutions to some types of parabolic Hessian equations, Kazuhiro Takimoto, Meeting of the Mathematical Society of Japan, 2015/09/15, With Invitation, Japanese, Kyoto Sangyo University
  15. Bernstein type theorem for the generalized parabolic $k$-Hessian equation, Kazuhiro Takimoto, Kyoto University NLPDE Seminar, 2015/10/23, With Invitation, Japanese, Kyoto University
  16. Entire solutions to the generalized parabolic $k$-Hessian equation, Kazuhiro Takimoto, Applied Analysis Seminar, 2015/11/07, With Invitation, Japanese, Kumamoto University
  17. On a Bernstein type theorem for some types of parabolic Hessian equations, Kazuhiro Takimoto, Asymptotic Problems for Partial Differential Equations and Viscosity Solutions, 2015/12/04, With Invitation, English, RIMS, Kyoto University
  18. Bernstein type theorem for some types of parabolic Hessian equations, Kazuhiro Takimoto, The 33rd Kyushu Symposium on Partial Differential Equations, 2016/01/27, With Invitation, English, Kyushu University Nishijin Plaza
  19. Bernstein type theorems for parabolic $k$-Hessian equations, Kazuhiro Takimoto, Maximum principles in partial differential equations and related topics, 2016/03/04, With Invitation, Japanese, Hokkaido University
  20. Entire solutions to generalized parabolic $k$-Hessian equations, Kazuhiro Takimoto, 11th AIMS International Conference on Dynamical Systems, Differential Equations and Applications, 2016/07/03, With Invitation, English, Hyatt Regency Orlando
  21. Some removability results for two classes of fully nonlinear PDEs, Kazuhiro Takimoto, Qualitative Theory on Nonlinear Partial Differential Equations, 2017/09/19, With Invitation, English, Okayama University
  22. On a Bernstein type theorem for some types of parabolic Hessian equations, Kazuhiro Takimoto, Capital Normal University-Hiroshima University Joint conference on Mathematics, 2017/09/22, With Invitation, English, Capital Normal University
  23. Some removability results for $k$-Hessian equation and $k$-curvature equation, Kazuhiro Takimoto, 12th AIMS International Conference on Dynamical Systems, Differential Equations and Applications, 2018/07/05, With Invitation, English, National Taiwan University
  24. Some removability results for k-Hessian equation and k-curvature equation, Kazuhiro Takimoto, 12th AIMS International Conference on Dynamical Systems, Differential Equations and Applications, 2018/07/05, With Invitation, English, National Taiwan University
  25. Kral type removability theorems for k-Hessian equation and k-curvature equation, Kazuhiro Takimoto, 4th Swiss-Japanese PDE Seminar, 2019/09/04, With Invitation, English, I-site Namba, Osaka Prefecture University
  26. Some removability results for $k$-Hessian equation and $k$-curvature equation, Kazuhiro Takimoto, The 17th Hamamatsu Conference on Partial Differential Equations, 2019/12/14, With Invitation, Japanese, Shizuoka University
  27. Bernstein type theorem for the parabolic 2-Hessian equation under weaker conditions, Kazuhiro Takimoto, Meeting of the Mathematical Society of Japan, 2020/09/22, Without Invitation, Japanese, Mathematical Society of Japan, Kumamoto University
  28. The exterior Dirichlet problem for the generalized parabolic $k$-Hessian equations, Kazuhiro Takimoto, Meeting of the Mathematical Society of Japan, 2021/03/16, Without Invitation, Japanese, Mathematical Society of Japan, Keio University
  29. Exact blowup rate near the boundary of boundary blowup solutions to k-Hessian equation, Kazuhiro Takimoto, Meeting of the Mathematical Society of Japan, 2021/09/14, Without Invitation, Japanese, Mathematical Society of Japan, Chiba University
  30. Asymptotic behavior near the boundary of boundary blowup solutions to $k$-Hessian equation and $k$-curvature equation, Kazuhiro Takimoto, Qualitative Theory of Ordinary Differential Equations and its Applications, 2021/11/10, With Invitation, Japanese, online
  31. Bernstein type theorem for the generalized parabolic 2-Hessian equation under weaker assumptions, Kazuhiro Takimoto, Kyushu Functional Equation Seminar, 2021/11/19, With Invitation, Japanese, online
  32. On a Bernstein type theorem for the parabolic 2-Hessian equation under weaker assumptions, Kazuhiro Takimoto, The 5th Workshop on the Behavior of Solutions to Reaction-Diffusion Equation and Nonlinear Dispersive Equation, 2022/02/17, With Invitation, Japanese, online
  33. Bernstein type theorem for the parabolic 2-Hessian equation under weaker assumptions, Kazuhiro Takimoto, Tuesday Seminar of Analysis, 2022/11/29, With Invitation, Japanese, University of Tokyo
    Related URL
  34. The exterior Dirichlet problem for the generalized parabolic k-Hessian equations, Kazuhiro Takimoto, Geometric Aspects on Partial Differential Equations, 2022/12/05, With Invitation, Japanese, RIMS, Kyoto University
    Related URL
  35. Blowup rate near the boundary of boundary blowup solutions to $k$-Hessian equation and $k$-curvature equation, Kazuhiro Takimoto, 13th AIMS International Conference on Dynamical Systems, Differential Equations and Applications, 2023/06/01, With Invitation, English, University of North Carolina Wilmington
  36. Higher order estimate near the boundary of a large solution to semilinear Poisson equation with double-power like nonlinearity, Kazuhiro Takimoto and Yuxao Zhang, Meeting of the Mathematical Society of Japan, 2023/09/20, Without Invitation, Japanese, Mathematical Society of Japan, Tohoku University
  37. On the exterior Dirichlet problem for the generalized parabolic k-Hessian equations, Kazuhiro Takimoto, 2024 Japan-Korea Workshop on Nonlinear PDEs and Its Applications, 2024/01/16, With Invitation, English, Hiroshima University
    Related URL

External Funds

Acceptance Results of Competitive Funds

  1. KAKENHI, Solvability of Boundary Value Problems and Analysis on the Behavior of Solutions of Fully Nonlinear Elliptic and Parabolic Partial Differential Equations, 2004/04/01, 2007/03/31
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  2. KAKENHI, Analysis on Fully Nonlinear Elliptic and Parabolic Partial Differential Equations and its Applications, 2010/04/01, 2013/03/31
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  3. Hiroshima University Fujii Research Fund, Analysis on the Solvability of Boundary Value Problem and the Behavior of Solutions to Fully Nonlinear Partial Differential Equations, 2010/11/01, 2012/10/31
  4. KAKENHI, Analysis on Behavior and Singularities of Solutions to Fully Nonlinear Elliptic and Parabolic Partial Differential Equations, 2013/04/01, 2017/03/31
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  5. KAKENHI, Research on the Quantitative Properties and the Singularities for Solutions to k-Hessian equations and k-curvature equations, 2022/04/01, 2026/03/31
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Social Activities

Organizing Academic Conferences, etc.

  1. HMA Special Seminar, 2007 Winter, Organizer, 2007/01, 2007/01
  2. Workshop on Differential Equations in Hiroshima, Organizer, 2007/10, 2007/10
  3. Dynamical Systems and Differential Equations, Organizer, 2007/11, 2007/11
  4. International Workshop on Global Behaviors of Differential Equations -- Singularity and Transformation Theory --, Organizer, 2008/09, 2008/09
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  5. Workshop on Differential Equations in Hiroshima, Organizer, 2008/10, 2008/10
  6. HMA Special Seminar, 2010 Winter, Organizer, 2010/01, 2010/01
  7. Workshop on Differential Equations in Hiroshima, Organizer, 2010/10, 2010/10
  8. HMA Special Seminar, 2011 Winter, Organizer, 2011/01, 2011/01
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  9. Workshop on Differential Equations in Hiroshima, Organizer, 2011/10, 2011/10
  10. Mathematical Approaches for Ecosystem Research, Organizer, 2012/02, 2012/02
  11. Nonlinear Partial Differential Equations, Dynamical Systems and Their Applications, Organizer, 2012/09, 2012/09
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  12. Workshop on Differential Equations in Hiroshima, Organizer, 2012/10, 2012/10
  13. HMA Special Seminar, 2013 Winter, Organizer, 2013/01, 2013/01
  14. Workshop on Differential Equations in Hiroshima, Organizer, 2013/10, 2013/10
  15. Mathematical Analysis of Pattern Formation Arising in Nonlinear Phenomena, Organizer, 2013/10, 2013/11
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  16. HMA Special Seminar, 2014 Winter, Organizer, 2014/01, 2014/01
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  17. MSJ Autumn Meeting 2014, Organizer, 2014/09, 2014/09
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  18. Workshop on Differential Equations in Hiroshima, Organizer, 2014/10, 2014/10
  19. International Conference on Recent Advances in Hyperbolic Partial Differential Equations, Organizer, 2014/12, 2014/12
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  20. HMA Special Seminar, 2015 Winter, Organizer, 2015/01, 2015/01
  21. Workshop on Differential Equations in Hiroshima, Organizer, 2015/10, 2015/10
  22. HMA Special Seminar, 2016 Winter, Organizer, 2016/01, 2016/01
  23. Workshop on Differential Equations in Hiroshima, Organizer, 2016/10, 2016/10
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  24. HMA Special Seminar, 2017 Winter, Organizer, 2017/01, 2017/01
  25. Qualitative Theory on Nonlinear Partial Differential Equations, Organizer, 2017/09, 2017/09
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  26. Workshop on Differential Equations in Hiroshima, Organizer, 2017/10, 2017/10
  27. HMA Special Seminar, 2018 Winter, Organizer, 2018/01, 2018/01
  28. Workshop on Differential Equations in Hiroshima, Organizer, 2018/10, 2018/10
  29. HMA Special Seminar, 2019 Winter, Organizer, 2019/01, 2019/01
  30. HMA Special Seminar, 2020 Winter, Organizer, 2020/01, 2020/01
  31. Workshop on Differential Equations in Hiroshima, Organizer, 2021/10, 2021/10
  32. HMA Special Seminar, 2022 Winter, Organizer, 2022/01, 2022/01
  33. Workshop on Differential Equations in Hiroshima, Organizer, 2022/10, 2022/10
  34. HMA Special Seminar, 2023 Winter, Organizer, 2023/01, 2023/01
  35. Analysis of the Asymptotic Behavior on Differential Equations and its Related Topics, Organizer, 2023/03, 2023/03
  36. Takamatsu Workshop on Partial Differential Equations, Organizer, 2023/03, 2023/03
  37. Workshop on Differential Equations in Hiroshima, Organizer, 2023/10, 2023/10
  38. HMA Special Seminar, 2024 Winter, Organizer, 2024/01, 2024/01
  39. Takamatsu Workshop on Differential Equations and Related Topics, Organizer, 2024/03, 2024/03
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