Organization
School of Computing Associate Professor
Title
Associate Professor
External link
takahashi jin
Degree
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Doctor of Science ( Tokyo Institute of Technology )
Research Interests
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Blow-up solutions
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Singular solutions
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Diffusion equations
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Nonlinear parabolic equations
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Partial differential equations
Research Areas
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Natural Science / Mathematical analysis
Committee Memberships
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The Mathematical Society of Japan Editor, Sugaku Expositions
2019.7 - 2021.6
Papers
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Critical norm blow-up rates for the energy supercritical nonlinear heat equation Reviewed
Tobias Barker, Hideyuki Miura, Jin Takahashi
to appear in Journal of Functional Analysis 2026
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Critical norm blow-up for the energy supercritical nonlinear heat equation Reviewed
Hideyuki Miura, Jin Takahashi
to appear in American Journal of Mathematics 2026
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Moving gradient singularity for the evolutionary p-Laplace equation Reviewed
Erik Lindgren, Jin Takahashi
Journal of Elliptic and Parabolic Equations 2025.4
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Solutions with moving singularities for a one-dimensional nonlinear diffusion equation Reviewed
Marek Fila, Jin Takahashi, Eiji Yanagida
Mathematische Annalen 2024.5
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On critical norm blow-up for a nonlinear heat equation Reviewed
Hideyuki Miura, Jin Takahashi
to appear in Proceedings of the conference "Critical Phenomena in Nonlinear Partial Differential Equations, Harmonic Analysis, and Functional Inequalities." 2024.5
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Blow-up of the critical norm for a supercritical semilinear heat equation Reviewed
Hideyuki Miura, Jin Takahashi
to appear in J. Eur. Math. Soc. 2023.10
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Initial traces and solvability for a semilinear heat equation on a half space of ℝ^{ℕ} Reviewed
Kotaro Hisa, Kazuhiro Ishige, Jin Takahashi
Transactions of the American Mathematical Society 2023.5
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Solvability of a semilinear heat equation on Riemannian manifolds Reviewed
Jin Takahashi, Hikaru Yamamoto
Journal of Evolution Equations 23 ( 2 ) 2023.4
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Infinite-time incompleteness of noncompact Yamabe flow Reviewed
Jin Takahashi, Hikaru Yamamoto
Calculus of Variations and Partial Differential Equations 61 ( 6 ) 212 - pp.24 2022
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Entire solutions with moving singularities for a semilinear heat equation with a critical exponent Reviewed
J. Takahashi
Partial Differ. Equ. Appl. 3 ( 29 ) 2022
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Anisotropic and isotropic persistent singularities of solutions of the fast diffusion equation Reviewed
M. Fila, P. Macková, J. Takahashi, E. Yanagida
Differential Integral Equations 35 ( 11-12 ) 729 - 748 2022
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Existence of solutions with moving singularities for a semilinear heat equation with a critical exponent Reviewed
J. Takahashi
J. Math. Pures. Appl. 148 128 - 149 2021
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On the heat equation with a dynamic Hardy-type potential Reviewed
J.-L. Chern, G. Hwang, J. Takahashi, E. Yanagida
J. Evol. Equ. 21 ( 2 ) 2141 - 2165 2021
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Solutions with snaking singularities for the fast diffusion equation Reviewed
M. Fila, J. R. King, J. Takahashi, E. Yanagida
Trans. Amer. Math. Soc. 374 8775 - 8792 2021
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Optimal singularities of initial data for solvability of the Hardy parabolic equation Reviewed
K. Hisa, J. Takahashi
J. Differential Equations 296 822 - 848 2021
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Moving singularities for nonlinear diffusion equations in two space dimensions Reviewed
M. Fila, P. Macková, J. Takahashi, E. Yanagida
J. Elliptic Parabol. Equ. 6 155 - 169 2020
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Existence of solutions for an inhomogeneous fractional semilinear heat equation Reviewed
K. Hisa, K. Ishige, J. Takahashi
Nonlinear Anal. 199 111920 - 28pp 2020
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Critical exponents for the fast diffusion equation with a nonlinear boundary condition Reviewed
R. Sato, J. Takahashi
482 123526 - 9pp 2020
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Solutions with moving singularities for equations of porous medium type Reviewed
M. Fila, J. Takahashi, E. Yanagida
Nonlinear Anal. 179 237 - 253 2019
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Solutions with time-dependent singular sets for the heat equation with absorption Reviewed
J. Takahashi, H. Yamamoto
J. Differential Equations 266 4061 - 4105 2019
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Higher-dimensional moving singularities in a superlinear parabolic equation Reviewed
K. P. P. HToo, J. Takahashi, E. Yanagida
J. Evol. Equ. 18 1575 - 1593 2018
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Time-dependent singularities in semilinear parabolic equations: Existence of solutions Reviewed
Toru Kan, Jin Takahashi
J. Differential Equations 263 ( 10 ) 6384 - 6426 2017.11
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Time-dependent singularities in a semilinear parabolic equation with absorption Reviewed
Jin Takahashi, Eiji Yanagida
COMMUNICATIONS IN CONTEMPORARY MATHEMATICS 18 ( 5 ) 1550077 - 27 pp. 2016.10
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Time-dependent singularities in semilinear parabolic equations: Behavior at the singularities Reviewed
Toni Kan, Jin Takahashi
JOURNAL OF DIFFERENTIAL EQUATIONS 260 ( 10 ) 7278 - 7319 2016.5
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Solvability of a Semilinear Parabolic Equation with Measures as Initial Data Reviewed
Jin Takahashi
GEOMETRIC PROPERTIES FOR PARABOLIC AND ELLIPTIC PDE'S 176 257 - 276 2016
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TIME-DEPENDENT SINGULARITIES IN THE HEAT EQUATION Reviewed
Jin Takahashi, Eiji Yanagida
COMMUNICATIONS ON PURE AND APPLIED ANALYSIS 14 ( 3 ) 969 - 979 2015.5
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On the profile of solutions with time-dependent singularities for the heat equation Reviewed
Toru Kan, Jin Takahashi
Kodai Math. J. 37 568 - 585 2014
MISC
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Asymptotic profiles of solutions for a diffusion equation with a dynamic Hardy potential
Jin Takahashi, Eiji Yanagida
preprint 2025
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Blow-up rate for the subcritical semilinear heat equation in non-convex domains
Hideyuki Miura, Jin Takahashi, Erbol Zhanpeisov
preprint 2025
Awards
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The 2018 MSJ Takebe Katahiro Prize for Encouragement of Young Researchers
2018.9 The Mathematical Society of Japan Moving singularities for parabolic equations
Jin Takahashi
Research Projects
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Analysis of formation and extinction of singularities in nonlinear parabolic equations
Grant number：23K12998 2023.4 - 2027.3
Japan Society for the Promotion of Science Grants-in-Aid for Scientific Research Grant-in-Aid for Early-Career Scientists
Grant amount：\4550000 （ Direct Cost: \3500000 、 Indirect Cost：\1050000 ）
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New trends in parabolic equations with nonlocal structures
Grant number：22KK0035 2022.10 - 2027.3
Japan Society for the Promotion of Science Grants-in-Aid for Scientific Research Fund for the Promotion of Joint International Research (Fostering Joint International Research (B))
Grant amount：\20150000 （ Direct Cost: \15500000 、 Indirect Cost：\4650000 ）
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Analysis of dynamic singularities in parabolic partial differential equations
Grant number：22H01131 2022.4 - 2027.3
Japan Society for the Promotion of Science Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (B)
Grant amount：\16770000 （ Direct Cost: \12900000 、 Indirect Cost：\3870000 ）
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放物型方程式における解の特異性保持メカニズムの解明
Grant number：19K14567 2019.4 - 2023.3
日本学術振興会 科学研究費助成事業 若手研究
高橋 仁
Grant amount：\4160000 （ Direct Cost: \3200000 、 Indirect Cost：\960000 ）
引き続き半線形熱方程式とfast diffusion方程式を主な対象とし，以下の研究を行なった．半線形熱方程式については非線形項に特異性を持ついわゆるHardyポテンシャルを付したものに対し，可解性が得られるための最も強い特異性を特定した．この研究は比佐幸太郎氏(東京大学)との共同研究であり，すでに論文が出版済みである．Fast diffusion方程式については，M. Fila氏(Comenius Univeristy, Slovakia), P. Mackova氏(Comenius Univeristy, Slovakia), 柳田英二氏(東京大学)との共同研究により特異点近傍で異方性を持つ解を構成した．また，山本光氏(筑波大学)との共同研究により非コンパクト山辺流の解の完備性の破れに関する結果も得られた．これらはすでに論文としてまとめ，投稿中である．