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J-GLOBAL ID：200901055738922864
Update date: Jan. 30, 2024
Ishii Katsuyuki
イシイ カツユキ | Ishii Katsuyuki
Affiliation and department：
Job title：
Professor
Research field (1)：
Mathematical analysis
Research keywords (1)：
Nonlinear analysis
Research theme for competitive and other funds (41)：
- 2023 - 2028 Canonical mean curvature flow and its application to evolution problems
- 2019 - 2024 表面拡散方程式によって時間発展する曲線・曲面の形状と特異性の解析
- 2020 - 2023 曲面・曲線からなる曲率流に対する近似アルゴリズムとそれを用いた広義解の性質の研究
- 2018 - 2023 Multifaceted studies on dynamical problems in the calculus of variations using geometric measure theory
- 2017 - 2020 曲率によって動く曲線・曲面に対する数値計算アルゴリズムとその正則性・特異性
- 2015 - 2018 Deepening and application of a theory for the logarithmic Sobolev inequality
- 2014 - 2018 Critical exponent and the behavior of solutions to nonlinear parabolic partial differential equations
- 2013 - 2018 Variational analysis on dynamic geometric problems
- 2013 - 2016 Well-posedness for nonautonomous differential systems with dissipativity structure described by metric-like functionals
- 2011 - 2016 Fundamental theory for viscosity solutions of fully nonlinear equations and its applications
- 2011 - 2016 Deepening of the theory of viscosity solutions and its applications
- 2012 - 2015 Study for Hamilton-Jacobi equations and logarithmic Sobolev inequality
- 2011 - 2015 Singularity of solutions for nonlinear partial differential equations of parabolic type and structure of solutions for the stationary problems
- 2012 - 2015 平均曲率流に対する近似問題と正則性・特異性に関する研究
- 2009 - 2011 New development and its application of Aubry-Mather theory for Hamilton-Jacobi equations
- 2008 - 2010 Self-similarity and singularity of solutions for nonlinear parabolic PDEs
- 2008 - 2010 Viscosity solution theory for fully nonlinear equations and its applications
- 2006 - 2009 Analysis on anisotropic curvature flow equations in phenomena
- 2006 - 2009 RESEARCH ON THE THEORY OF VISCOSITY SOLUTIONS OF DIFFERENTIAL EQUATIONS AND ITS APPLICATIONS
- 2006 - 2008 Study on asymptotic solutions of Hamilton-Jacobi equations based on the theory of viscosity solutions
- 2006 - 2008 Mathematical analysis for phenomena in the living body and its simulation
- 2008 - 平均曲率流の近似問題と正則性・特異性に関する研究
- 2004 - 2007 On the study of the theory of viscosity solutions and its new developments
- 2003 - 2005 画像処理の数理における実解析的手法の探索
- 2003 - 2005 Mathematical modeling and analysis for phenomena in medical science
- 2003 - 2005 Research on the theory of viscosity solutions and its applications
- 2005 - Rでの非線形退化楕円型偏微分方程式の非有界な粘性解の構造の研究
- 2005 - 非線形放物型偏微分方程式の自己相似構造と解の特異性
- 2005 - 非線形発展方程式の最適制御と逆問題解析の研究
- 2005 - 数値計算アルゴリズムを用いた平均曲率流の解析的研究
- 2002 - 2004 Studies on the applications of the theory of viscosity solutions to some singular perturbation problems
- 2001 - 2003 Study of viscosity solutions for partial differential equations with subdifferential
- 2000 - 2002 Research on viscosity solutions of differential equations and their applications
- 1998 - 2001 viscosity solutions of nonlinear partial differential equations with singularities
- 1997 - 2000 On symmetric and radial viscosity solutions for elliptic partial differential equation.
- 1998 - 1999 Research in viscosity solutions using the method of Functional Analysis.
- 1997 - 1999 Asymptotics of the solutions of nonlinear partial differential equations and their applications to phase transition
- 1997 - 1999 Theory and applications of viscosity solutions
- 1994 - 1994 関数解析的方法方法による非線型波動方程式の研究
- 1993 - 1993 二階非線形偏微分方程式に対する粘性解の研究
- 1992 - 1992 関数解析的方法による発展方程式の研究
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Papers (26)：
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Katsuyuki Ishii, Michel Pierre, Takashi Suzuki. Quasilinear Parabolic Equations Associated with Semilinear Parabolic Equations. Mathematics. 2023. 11. 3. 758-758
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Katsuyuki Ishii. Convergence of a threshold-type algorithm for curvature-dependent motions of hypersurfaces. Advanced Studies in Pure Mathematics. 2020. 85. 181-191
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Katsuyuki Ishii, Takahiro Izumi. Remarks on the convergence of an algorithm for curvature-dependent motions of hypersurfaces. Discrete and Continuous Dynamical Systems- Series A. 2018. 38. 3. 1103-1125
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K. Ishii, H. Kamata, S. Koike. Remarks on viscosity solutions for mean curvature flow with obstacles. Springer Proceedings in Mathematics and Statistics. 2017. 215. 83-103
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Katsuyuki Ishii, Masato Kimura. Convergence of a threshold-type algorithm using the signed distance function. INTERFACES AND FREE BOUNDARIES. 2016. 18. 4. 479-522
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MISC (10)：
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Ishii Katsuyuki. Rate of convergence of an algorithm for curvature-dependent motions of hypersurfaces (Reconsideration of the method of estimates on partial differential equations from a point of view of the theory on abstract evolution equations). RIMS Kokyuroku. 2016. 1984. 152-163
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Ishii Katsuyuki. On the convergence of an area minimizing scheme for the anisotropic mean curvature flow (New developments of the theory of evolution equations in the analysis of non-equilibria). RIMS Kokyuroku. 2013. 1856. 102-112
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Ishii Katsuyuki. Rate of convergence of the Bence-Merriman-Osher algorithm for motion by mean curvature(Viscosity Solution Theory of Differential Equations and its Developments). RIMS Kokyuroku. 2006. 1481. 11-19
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Ishii Katsuyuki. Nonlinear second order elliptic equations with subdifferential terms (Viscosity Solutions of Differential Equations and Related Topics). RIMS Kokyuroku. 2002. 1287. 155-163
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Ishii Katsuyuki. Interior regularity of viscosity solutions for nonlinear second order ellitic partial differential equations (Studies on qualitative estimates on regularity and singularity of solutions of PDEs). RIMS Kokyuroku. 2002. 1242. 40-49
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Books (1)：
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Image processing and curvature flow equations
Saiensu=sha Co., Ltd. Publishers 2008
Lectures and oral presentations (45)：
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Approximate problems of a threshold-type to mean curvature flow
(Workshop on applied mathematics 2018 2018)
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Convergence of a threshold-type algorithm to mean curvature flow
(Conference on elliptic/parabolic differential equations 2018)
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Convergence of a threshold-type algorithm to curvature-dependent motions
(Viscosity solutions and Related Topics 2018)
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Convergence of a threshold-type algorithm for mean curvature flow
(The 11th Mathematical Society of Japan (MSJ) Seasonal Institute (SI) The Role of Metrics in the Theory of Partial Differential Equations 2018)
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Convergence of a threshold-type algorithm for mean curvature flow
(12th AIMS on Dynamical Systems, Differential Equations and Applications 2018)
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Education (1)：
- - 1991 Kobe University Graduate School of Science and Technology
Professional career (2)：
- 理学修士 (神戸大学)
- 博士(理学) (神戸大学)
Association Membership(s) (1)：
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