# 髙棹 圭介

プロフィール
(日本語)

(英語)
My research object is a geometrical partial differential equation related to the minimal surface and the mean curvature flow. Since singularity can occur in the solution, I am constructing a weak solution by using the geometric measure theory. With regard to education, I try to explain using motives of problems and easy-to-understand examples to deepen understanding of mathematical matters.
researchmap URL
https://researchmap.jp/7000021256

(日本語)

(英語)
My research theme is the mathematical analysis of partial differential equations that have hypersurfaces with singularities as solutions. I am interested in the existence, uniqueness and regularity of the solutions of such equations in the weak sense. Moreover I am interested in the stability of the stationary solutions and methods of constructing the solutions such as the phase field method.

(日本語)

(英語)
For the evolution equation of the hypersurface such as the mean curvature flow equation, the following problem is addressed: (1) Proof of existence of a weak solution called Brakke flow, especially proof that an approximate solution obtained by the phase field method converges to a weak solution in the sense of Brakke flow. (2) Derivation of energy estimates such as Huisken's monotonicity formula of the mean curvature flow on the obtained solutions. (3) Problems of the surface evolution equations with the conservation law such as volume preservation conditions. (4) Boundary value problem for the Brakke flow such as the dynamic boundary condition.

キーワード(日本語) キーワード(英語)

Yoshikazu Giga, Fumihiko Onoue, Keisuke Takasao Yoshikazu Giga, Fumihiko Onoue, Keisuke Takasao A varifold formulation of mean curvature flow with Dirichlet or dynamic boundary conditions A varifold formulation of mean curvature flow with Dirichlet or dynamic boundary conditions A varifold formulation of mean curvature flow with Dirichlet or dynamic boundary conditions Differential Integral Equations, 34, 1--2, 21-16 , 34, 1--2, 21-16 Differential Integral Equations, 34, 1--2, 21-16 2021/01 英語 研究論文(学術雑誌)
Keisuke Takasao Keisuke Takasao Keisuke Takasao Global existence and monotonicity formula for volume preserving mean curvature flow Global existence and monotonicity formula for volume preserving mean curvature flow Global existence and monotonicity formula for volume preserving mean curvature flow RIMS Kôkyûroku Bessatsu, B80, 81-94 RIMS Kôkyûroku Bessatsu, B80, 81-94 RIMS Kôkyûroku Bessatsu, B80, 81-94 2020 英語
Keisuke Takasao Keisuke Takasao Keisuke Takasao Existence of weak solution for mean curvature flow with transport term and forcing term Existence of weak solution for mean curvature flow with transport term and forcing term Existence of weak solution for mean curvature flow with transport term and forcing term Communications on Pure & Applied Analysis, 19, 5, 2655-2677 Communications on Pure & Applied Analysis, 19, 5, 2655-2677 Communications on Pure & Applied Analysis, 19, 5, 2655-2677 2020 英語 研究論文(学術雑誌)
Keisuke Takasao Keisuke Takasao Keisuke Takasao CONVERGENCE OF THE ALLEN-CAHN EQUATION WITH CONSTRAINT TO BRAKKE'S MEAN CURVATURE FLOW CONVERGENCE OF THE ALLEN-CAHN EQUATION WITH CONSTRAINT TO BRAKKE'S MEAN CURVATURE FLOW CONVERGENCE OF THE ALLEN-CAHN EQUATION WITH CONSTRAINT TO BRAKKE'S MEAN CURVATURE FLOW ADVANCES IN DIFFERENTIAL EQUATIONS, 22, 9-10, 765-792 ADVANCES IN DIFFERENTIAL EQUATIONS, 22, 9-10, 765-792 ADVANCES IN DIFFERENTIAL EQUATIONS, 22, 9-10, 765-792 2017/09 英語 研究論文(学術雑誌)
Masashi Mizuno, Keisuke Takasao Masashi Mizuno, Keisuke Takasao Masashi Mizuno, Keisuke Takasao Gradient estimates for mean curvature flow with Neumann boundary conditions Gradient estimates for mean curvature flow with Neumann boundary conditions Gradient estimates for mean curvature flow with Neumann boundary conditions NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS, 24, 4 NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS, 24, 4 NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS, 24, 4 2017/08 英語 研究論文(学術雑誌)
Keisuke Takasao Keisuke Takasao Keisuke Takasao Existence of Weak Solution for Volume-Preserving Mean Curvature Flow via Phase Field Method Existence of Weak Solution for Volume-Preserving Mean Curvature Flow via Phase Field Method Existence of Weak Solution for Volume-Preserving Mean Curvature Flow via Phase Field Method INDIANA UNIVERSITY MATHEMATICS JOURNAL, 66, 6, 2015-2035 INDIANA UNIVERSITY MATHEMATICS JOURNAL, 66, 6, 2015-2035 INDIANA UNIVERSITY MATHEMATICS JOURNAL, 66, 6, 2015-2035 2017 英語 研究論文(学術雑誌)
Keisuke Takasao, Yoshihiro Tonegawa Keisuke Takasao, Yoshihiro Tonegawa Keisuke Takasao, Yoshihiro Tonegawa Existence and regularity of mean curvature flow with transport term in higher dimensions Existence and regularity of mean curvature flow with transport term in higher dimensions Existence and regularity of mean curvature flow with transport term in higher dimensions MATHEMATISCHE ANNALEN, 364, 3-4, 857-935 MATHEMATISCHE ANNALEN, 364, 3-4, 857-935 MATHEMATISCHE ANNALEN, 364, 3-4, 857-935 2016/04 英語 研究論文(学術雑誌)
Tomoyuki Suzuki, Keisuke Takasao, Noriaki Yamazaki Tomoyuki Suzuki, Keisuke Takasao, Noriaki Yamazaki New approximate method for the Allen--Cahn equation with double-obstacle constraint and stability criteria for numerical simulations New approximate method for the Allen--Cahn equation with double-obstacle constraint and stability criteria for numerical simulations New approximate method for the Allen--Cahn equation with double-obstacle constraint and stability criteria for numerical simulations AIMS Mathematics, 1, 3, 288-317 AIMS Mathematics, 1, 3, 288-317 AIMS Mathematics, 1, 3, 288-317 2016 英語 研究論文(学術雑誌)
Tomoyuki Suzuki, Keisuke Takasao, Noriaki Yamazaki Tomoyuki Suzuki, Keisuke Takasao, Noriaki Yamazaki Remarks on numerical experiments of the Allen-Cahn equations with constraint via Yosida approximation Remarks on numerical experiments of the Allen-Cahn equations with constraint via Yosida approximation Remarks on numerical experiments of the Allen-Cahn equations with constraint via Yosida approximation Advances in Numerical Analysis Advances in Numerical Analysis Advances in Numerical Analysis 2016 英語 研究論文(学術雑誌)

Keisuke Takasao Keisuke Takasao Keisuke Takasao GRADIENT ESTIMATES AND EXISTENCE OF MEAN CURVATURE FLOW WITH TRANSPORT TERM GRADIENT ESTIMATES AND EXISTENCE OF MEAN CURVATURE FLOW WITH TRANSPORT TERM GRADIENT ESTIMATES AND EXISTENCE OF MEAN CURVATURE FLOW WITH TRANSPORT TERM DIFFERENTIAL AND INTEGRAL EQUATIONS, 26, 1-2, 141-154 DIFFERENTIAL AND INTEGRAL EQUATIONS, 26, 1-2, 141-154 DIFFERENTIAL AND INTEGRAL EQUATIONS, 26, 1-2, 141-154 2013/01 英語 研究論文(学術雑誌)
Keisuke Takasao Keisuke Takasao Keisuke Takasao Stability of travelling wave solutions for the Landau-Lifshitz Stability of travelling wave solutions for the Landau-Lifshitz Stability of travelling wave solutions for the Landau-Lifshitz HIROSHIMA MATHEMATICAL JOURNAL, 41, 3, 367-388 HIROSHIMA MATHEMATICAL JOURNAL, 41, 3, 367-388 HIROSHIMA MATHEMATICAL JOURNAL, 41, 3, 367-388 2011/11 英語 研究論文(学術雑誌)

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タイトル タイトル(日本語) タイトル(英語) 会議名 会議名(日本語) 会議名(英語) 主催者 主催者(日本語) 主催者(英語) 発表年月日 記述言語 会議種別
ある非局所項付きAllen-Cahn方程式を用いた体積保存平均曲率流の存在について[招待あり] ある非局所項付きAllen-Cahn方程式を用いた体積保存平均曲率流の存在について [招待あり] 九州関数方程式セミナー 九州関数方程式セミナー 2021/04/23 日本語 口頭発表(招待・特別)
Phase field model for mean curvature flow with transport term and forcing term[招待あり] Phase field model for mean curvature flow with transport term and forcing term [招待あり] Phase field model for mean curvature flow with transport term and forcing term [招待あり] 第4回反応拡散方程式と非線形分散型方程式の解の挙動 第4回反応拡散方程式と非線形分散型方程式の解の挙動 2021/02/17 日本語 口頭発表(招待・特別)
On obstacle problem for Brakke's mean curvature flow[招待あり] On obstacle problem for Brakke's mean curvature flow [招待あり] On obstacle problem for Brakke's mean curvature flow [招待あり] The 22nd Northeastern Symposium on Mathematical Analysis The 22nd Northeastern Symposium on Mathematical Analysis The 22nd Northeastern Symposium on Mathematical Analysis 2021/02/15 英語 口頭発表(招待・特別)
On obstacle problem for Brakke's mean curvature flow[招待あり] On obstacle problem for Brakke's mean curvature flow [招待あり] On obstacle problem for Brakke's mean curvature flow [招待あり] 第10回室蘭非線形解析研究会 第10回室蘭非線形解析研究会 2021/01/08 日本語 口頭発表(招待・特別)
Phase field method for volume preserving mean curvature flow[招待あり] Phase field method for volume preserving mean curvature flow [招待あり] Phase field method for volume preserving mean curvature flow [招待あり] Asia-Pacific Analysis and PDE Seminar Asia-Pacific Analysis and PDE Seminar Asia-Pacific Analysis and PDE Seminar 2020/12/07 英語 口頭発表(招待・特別)
Existence of weak solution for mean curvature flow with forcing term[招待あり] Existence of weak solution for mean curvature flow with forcing term [招待あり] Existence of weak solution for mean curvature flow with forcing term [招待あり] Workshop in Geometric Measure Theory and Applications Workshop in Geometric Measure Theory and Applications Workshop in Geometric Measure Theory and Applications 2020/12/05 英語 口頭発表(招待・特別)
On obstacle problem for Brakke flow[招待あり] On obstacle problem for Brakke flow [招待あり] On obstacle problem for Brakke flow [招待あり] 北海道大学偏微分方程式セミナー 北海道大学偏微分方程式セミナー 2020/10/09 英語 口頭発表(招待・特別)
フェイズフィールド法による外力項付き平均曲率流方程式の弱解の存在について[招待あり] フェイズフィールド法による外力項付き平均曲率流方程式の弱解の存在について [招待あり] 日本数学会2020年度秋季総合分科会 実函数論分科会 日本数学会2020年度秋季総合分科会 実函数論分科会 2020/09/25 日本語 口頭発表(招待・特別)
フェイズフィールド法による平均曲率流の弱解の存在について[招待あり] フェイズフィールド法による平均曲率流の弱解の存在について [招待あり] 談話会 談話会 京都大学数学教室、数理解析研究所 京都大学数学教室、数理解析研究所 2019/11/27 日本語 公開講演、セミナー、チュートリアル、講習、講義
Existence of weak solution for mean curvature flow with forcing term[招待あり] Existence of weak solution for mean curvature flow with forcing term [招待あり] Existence of weak solution for mean curvature flow with forcing term [招待あり] Oberseminar Analysis in Dortmund Oberseminar Analysis in Dortmund Oberseminar Analysis in Dortmund 2019/11/18 英語 公開講演、セミナー、チュートリアル、講習、講義

Existence of weak solution for mean curvature flow with forcing term[招待あり] Existence of weak solution for mean curvature flow with forcing term [招待あり] Existence of weak solution for mean curvature flow with forcing term [招待あり] Kanazawa workshop: Gradient flows and related topics: analysis and applications Kanazawa workshop: Gradient flows and related topics: analysis and applications Kanazawa workshop: Gradient flows and related topics: analysis and applications 2019/08/10 英語 口頭発表(招待・特別)
Phase field method for mean curvature flow with dynamic boundary condition[招待あり] Phase field method for mean curvature flow with dynamic boundary condition [招待あり] Phase field method for mean curvature flow with dynamic boundary condition [招待あり] 界面運動，力学系に現れる漸近問題への粘性解的手法とその周辺 界面運動，力学系に現れる漸近問題への粘性解的手法とその周辺 Viscosity solution approach to asymptotic problems in front propagation, dynamical system and related topics 2019/07/17 英語 口頭発表(招待・特別)

Phase field method for mean curvature flow with dynamic boundary condition[招待あり] Phase field method for mean curvature flow with dynamic boundary condition [招待あり] Phase field method for mean curvature flow with dynamic boundary condition [招待あり] 研究集会「数学と現象：Mathematics and Phenomena in Miyazaki 2018」 研究集会「数学と現象：Mathematics and Phenomena in Miyazaki 2018」 2018/11/16 日本語 口頭発表(一般)
Convergence of Landau-Lifshitz equation to multi-phase mean curvature flow[招待あり] Convergence of Landau-Lifshitz equation to multi-phase mean curvature flow [招待あり] Convergence of Landau-Lifshitz equation to multi-phase mean curvature flow [招待あり] 大阪大学 微分方程式セミナー 大阪大学 微分方程式セミナー 2018/06/22 日本語 口頭発表(招待・特別)

Remarks on convergence of vector-valued Allen-Cahn equation to multi-phase mean curvature flow[招待あり] Remarks on convergence of vector-valued Allen-Cahn equation to multi-phase mean curvature flow [招待あり] Remarks on convergence of vector-valued Allen-Cahn equation to multi-phase mean curvature flow [招待あり] 松山解析セミナー 2018 松山解析セミナー 2018 2018/02/02 日本語 口頭発表(招待・特別)
Rectifiability of varifolds in the singular limit of Allen-Cahn equation with non-local term[招待あり] Rectifiability of varifolds in the singular limit of Allen-Cahn equation with non-local term [招待あり] Rectifiability of varifolds in the singular limit of Allen-Cahn equation with non-local term [招待あり] 第13回 非線型の諸問題 第13回 非線型の諸問題 2017/09/20 日本語 口頭発表(招待・特別)
フェイズフィールド法によるBrakkeの平均曲率流の構成[招待あり] フェイズフィールド法によるBrakkeの平均曲率流の構成 [招待あり] 応用数学勉強会2017 応用数学勉強会2017 2017/08/23 日本語 公開講演、セミナー、チュートリアル、講習、講義
Phase field method for mean curvature flow with a non-local term[招待あり] Phase field method for mean curvature flow with a non-local term [招待あり] Phase field method for mean curvature flow with a non-local term [招待あり] Optimal Control and PDE Optimal Control and PDE Optimal Control and PDE 2017/07/21 英語 口頭発表(招待・特別)
Convergence of the Allen-Cahn equation with non-local term to the volume preserving mean curvature flow[招待あり] Convergence of the Allen-Cahn equation with non-local term to the volume preserving mean curvature flow [招待あり] Convergence of the Allen-Cahn equation with non-local term to the volume preserving mean curvature flow [招待あり] 第３７回 南大阪応用数学セミナー 第３７回 南大阪応用数学セミナー 2017/06/10 英語 口頭発表(招待・特別)
Existence of weak solutions for mean curvature flow with a non-local term[招待あり] Existence of weak solutions for mean curvature flow with a non-local term [招待あり] Existence of weak solutions for mean curvature flow with a non-local term [招待あり] RIMS 共同研究（公開型） 『偏微分方程式の解の形状解析』 RIMS 共同研究（公開型） 『偏微分方程式の解の形状解析』 2017/06/06 英語 口頭発表(招待・特別)

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