KURATA Kazuhiro
教授
倉田 和浩 クラタ カズヒロ くらた かずひろ
プロフィール
最終学歴・学位
東京大学大学院相関理化学研究科修士課程 1986年修了, 博士学位(数理科学)1993年,東京大学
専門・研究分野
数学,解析学,偏微分方程式, 非線型解析
研究
研究テーマ
線形偏微分方程式および非線形偏微分方程式の解の構造の研究,特に数理生態学や量子物理に現れる非線形変分問題の解の定性的および定量的な研究や固有値最適化問題など無限次元における最適化問題の研究.
研究キーワード
偏微分方程式, 変分問題, 固有値最適化問題, 非線形現象の数理
研究紹介
詳細情報
(著書)
1. 「フーリエ解析の基礎と応用」(倉田和浩, 単著), 数理工学社, 2020, 227pages. ISBN978-4-86481-067-8
2.「楕円型・放物型偏微分方程式」(村田實, 倉田和浩,共著), 岩波書店, 2006, 258pages. ISBN4-00-005650-6
(論文)
1.(with Ryusei yamashita)
Reconstruction of the defect by the enclosure method for inverse problems of the magnetic Schrödinger operator
Tokyo J. of Mathematics, 45(2) 547-577, 2022
2.(with Yuki Osad) Variational problems associated with a system of nonlinear Schrödinger equations with three wave interaction
Disc. Conti. Dyna. Sys., 27(3) 1511-1547, 2022
3.(with Yuki Osada) Asymptotic expansion of the ground state energy for nonlinear Schrödinger system with three wave interaction
Communications on Pure and Applied Analysis, 20(12) 4239-4239, 2021
4.(with Ishii, Yuta) Existence of multi-peak solutions to the Schnakenberg model with heterogeneity on metric graphs. Commun. Pure Appl. Anal. 20 (2021), no. 4, 1633–1679.
5. (with Masataka Shibata), Least energy solutions to semi-linear elliptic problems on metric graphs. J. Math. Anal. Appl. 491 (2020), no. 1, 124297, 22 pp.
6. (with T. Kajiwara), A Singular Perturbation Problem for heteroclinic Solutions to the FitzHugh-Nagumo Type Reaction-Diffusion System with heterogeneity, J. Math. Sci. Univ. Tokyo, vol.26(2019), 141-199.
7.(with Y. Ishii) Existence and stability of one-peak symmetric stationary solutions for the Schnakenberg model with heterogeneity, Discrete and Conti. Dynamical System, Series-A. vol. 35, no.5(2019), 2807-2875.
8.(with T. Kajiwara) On a Variational Problem Arising from the Three-component FitzHugh-Nagumo Type Reaction-Diffusion Systems, Tokyo J. Math. , 41, no.1 (2018), 131-174. DOI: 10.3836/tjm/1502179257
9.(with S.Jimbo) Asymptotic behavior of eigenvalues of the Laplacian on a thin domain under the mixed boundary condition,
Indiana University Mathematics Journal 65(3) 867-898(2016)
10. (with K. Morimoto) Existence of multiple spike stationary patterns in a chemotaxis model with weak saturation, Discrete Contin. Dyn. Syst. 31(1) 139-164(2011)
11.(with H. Matsuzawa) Multiple stable patterns in a balanced bistable equation with heterogeneous environments, Appl. Anal. 89(7) 1023-1035(2010)
12. (with S. Kawashima) Hardy type inequality and application to the stability of degenerate stationary waves, J. Functional Analysis 257(1) 1-19(2009)
13.(with Junping Shi) Optimal Spatial Harvesting Strategy and Symmetry Breaking Applied Math. Optim., Vol.58(2008), 89-110.
14.(with T. Ide, K. Tanaka) Multiple stable patterns for some reaction-diffusion equation in disrupted environments, Discrete and Continuous Dynamical Systems, vol.14, No.1, 93--116(2006).
15.(with M. Shibata, K. Tada) Existence of positive solutions for some nonlinear elliptic equations on unbounded domains with cylindrical ends Nonlinear Analysis 55 (2003)83--101.
16.(with E.M.Harrell II, P.Kroger) On the placement of an obstacle or a well so as to optimize the fundamental eigenvalue SIAM J.Math.Anal. 33 (2001), 240--25110.
17.(with S.Chanillo, D.Grieser, M.Imai, I.Ohnishi) Symmetry breaking and other phenomena in an eigenvalue optimization problem, Comm. Math. Phys.214 (2000), 315--337.
18.Existence and semi-classical limit of the least energy solution to a nonlinear Schrodinger equation with electromagnetic fields Nonlinear Anal. 41 (2000), 763--778.
1. 「フーリエ解析の基礎と応用」(倉田和浩, 単著), 数理工学社, 2020, 227pages. ISBN978-4-86481-067-8
2.「楕円型・放物型偏微分方程式」(村田實, 倉田和浩,共著), 岩波書店, 2006, 258pages. ISBN4-00-005650-6
(論文)
1.(with Ryusei yamashita)
Reconstruction of the defect by the enclosure method for inverse problems of the magnetic Schrödinger operator
Tokyo J. of Mathematics, 45(2) 547-577, 2022
2.(with Yuki Osad) Variational problems associated with a system of nonlinear Schrödinger equations with three wave interaction
Disc. Conti. Dyna. Sys., 27(3) 1511-1547, 2022
3.(with Yuki Osada) Asymptotic expansion of the ground state energy for nonlinear Schrödinger system with three wave interaction
Communications on Pure and Applied Analysis, 20(12) 4239-4239, 2021
4.(with Ishii, Yuta) Existence of multi-peak solutions to the Schnakenberg model with heterogeneity on metric graphs. Commun. Pure Appl. Anal. 20 (2021), no. 4, 1633–1679.
5. (with Masataka Shibata), Least energy solutions to semi-linear elliptic problems on metric graphs. J. Math. Anal. Appl. 491 (2020), no. 1, 124297, 22 pp.
6. (with T. Kajiwara), A Singular Perturbation Problem for heteroclinic Solutions to the FitzHugh-Nagumo Type Reaction-Diffusion System with heterogeneity, J. Math. Sci. Univ. Tokyo, vol.26(2019), 141-199.
7.(with Y. Ishii) Existence and stability of one-peak symmetric stationary solutions for the Schnakenberg model with heterogeneity, Discrete and Conti. Dynamical System, Series-A. vol. 35, no.5(2019), 2807-2875.
8.(with T. Kajiwara) On a Variational Problem Arising from the Three-component FitzHugh-Nagumo Type Reaction-Diffusion Systems, Tokyo J. Math. , 41, no.1 (2018), 131-174. DOI: 10.3836/tjm/1502179257
9.(with S.Jimbo) Asymptotic behavior of eigenvalues of the Laplacian on a thin domain under the mixed boundary condition,
Indiana University Mathematics Journal 65(3) 867-898(2016)
10. (with K. Morimoto) Existence of multiple spike stationary patterns in a chemotaxis model with weak saturation, Discrete Contin. Dyn. Syst. 31(1) 139-164(2011)
11.(with H. Matsuzawa) Multiple stable patterns in a balanced bistable equation with heterogeneous environments, Appl. Anal. 89(7) 1023-1035(2010)
12. (with S. Kawashima) Hardy type inequality and application to the stability of degenerate stationary waves, J. Functional Analysis 257(1) 1-19(2009)
13.(with Junping Shi) Optimal Spatial Harvesting Strategy and Symmetry Breaking Applied Math. Optim., Vol.58(2008), 89-110.
14.(with T. Ide, K. Tanaka) Multiple stable patterns for some reaction-diffusion equation in disrupted environments, Discrete and Continuous Dynamical Systems, vol.14, No.1, 93--116(2006).
15.(with M. Shibata, K. Tada) Existence of positive solutions for some nonlinear elliptic equations on unbounded domains with cylindrical ends Nonlinear Analysis 55 (2003)83--101.
16.(with E.M.Harrell II, P.Kroger) On the placement of an obstacle or a well so as to optimize the fundamental eigenvalue SIAM J.Math.Anal. 33 (2001), 240--25110.
17.(with S.Chanillo, D.Grieser, M.Imai, I.Ohnishi) Symmetry breaking and other phenomena in an eigenvalue optimization problem, Comm. Math. Phys.214 (2000), 315--337.
18.Existence and semi-classical limit of the least energy solution to a nonlinear Schrodinger equation with electromagnetic fields Nonlinear Anal. 41 (2000), 763--778.
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研究室
8号館632号室
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水曜3時限
内線番号
内線3141
メールアドレス
kurata●tmu.ac.jp
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