論文

• Kotaro Hisa, Kazuhiro Ishige, Jin Takahashi. Initial traces and solvability for a semilinear heat equation on a half space of R^N, Transactions of the American Mathematical Society, May 2023.
• Jin Takahashi, Hikaru Yamamoto. Solvability of a semilinear heat equation on Riemannian manifolds, Journal of Evolution Equations, Apr. 2023.
• M. Fila, P. Mackova, J. Takahashi, E. Yanagida. Anisotropic and isotropic persistent singularities of solutions of the fast diffusion equation, Differential Integral Equations, 35, Nov. 2022.
• Jin Takahashi, Hikaru Yamamoto. Infinite-time incompleteness of noncompact Yamabe flow, Calculus of Variations and Partial Differential Equations, Vol. 61, No. 6, Oct. 2022.
• J. Takahashi. Entire solutions with moving singularities for a semilinear heat equation with a critical exponent, Partial Differ. Equ. Appl., 3, 16, Mar. 2022.
• M. Fila, J. R. King, J. Takahashi, E. Yanagida. Solutions with snaking singularities for the fast diffusion equation, Trans. Amer. Math. Soc., 374, 8775--8792, Dec. 2021.
• K. Hisa, J. Takahashi. Optimal singularities of initial data for solvability of the Hardy parabolic equation, J. Differential Equations, 296, 822--848, Sept. 2021.
• Jin takahashi. Existence of solutions with moving singularities for a semilinear heat equation with a critical exponent, J. Math. Pures Appl., 148, 128--149, Apr. 2021.
• J.-L. Chern, G. Hwang, J. Takahashi, E. Yanagida. On the evolution equation with a dynamic Hardy-type potential, J. Evol. Equ., 21, 2141--2165, Feb. 2021.
• K. Hisa, K. Ishige, J. Takahashi. Existence of solutions for an inhomogeneous fractional semilinear heat equation, Nonlinear Anal., 199, 28, Oct. 2020.
• M. Fila, P. Mackova, J. Takahashi, E. Yanagida. Moving singularities for nonlinear diffusion equations in two space dimensions, J. Elliptic Parabol. Equ., 6, 155--169, Mar. 2020.
• R. Sato, J. Takahashi. Critical exponents for the fast diffusion equation with a nonlinear boundary condition, J. Math. Anal. Appl., 482, 9, Feb. 2020.
• Marek Fila, Jin Takahashi, Eiji Yanagida. Solutions with moving singularities for equations of porous medium type, Nonlinear Anal., 179, 237--253, Feb. 2019.
• Jin Takahashi, Hikaru Yamamoto. Solutions with time-dependent singular sets for the heat equation with absorption, J. Differential Equations, to appear. Online: Sep., 2018, Sept. 2018.
• Khin Phyu Phyu Htoo, Jin Takahashi, Eiji Yanagida. Higher-dimensional moving singularities in a superlinear parabolic equation, J. Evol. Equ., to appear. Online: May, 2018, May 2018.
• Toru Kan, Jin Takahashi. Time-dependent singularities in semilinear parabolic equations: Existence of solutions, J. Differential Equations, 263, 6384--6426, Nov. 2017.
• Jin Takahashi, Eiji Yanagida. Time-dependent singularities in a semilinear parabolic equation with absorption, Commun. Contemp. Math., 18, 15550077, 27 pp, Oct. 2016.
• Jin Takahashi. Solvability of a semilinear parabolic equation with measures as initial data, Springer Proc. Math. Stat., 176, 257--276, Aug. 2016.
• Toru Kan, Jin Takahashi. Time-dependent singularities in semilinear parabolic equations: Behavior at the singularities, J. Differential Equations, 260, 7278--7319, May 2016.
• Jin Takahashi, Eiji Yanagida. Time-dependent singularities in the heat equation, Commun. Pure Appl. Anal., 14, 969--979, May 2015.
• Toru Kan, Jin Takahashi. On the profile of solutions with time-dependent singularities for the heat equation, Kodai Math. J., 37, 568--585, Oct. 2014.
• Jin Takahashi. Time-dependent singularities in the heat equation (Geometry of solutions of partial differential equations), 数理解析研究所講究録, 京都大学, Vol. 1896, pp. 1-11, May 2014.

国際会議発表 (査読なし・不明)

• Jin Takahashi. Critical norm blow-up for a supercritical semilinear heat equation, Workshop on Elliptic & Parabolic PDEs 2023, Nov. 2023.
• Jin Takahashi. Critical norm blow-up for a supercritical semilinear heat equation, Euro-Japanese conference on nonlinear diffusions, Oct. 2023.
• Jin Takahashi. Critical norm blow-up for a supercritical semilinear heat equation, The 13th AIMS Conference on Dynamical Systems, Differential Equations And Applications, June 2023.
• Jin Takahashi. Blow-up of the critical norm for a supercritical semilinear heat equation, PDE seminar, Feb. 2023.
• Jin Takahashi. Critical norm blow-up for a supercritical semilinear heat equation, Seminar on Qualitative Theory of Differential Equations, Oct. 2022.
• Jin Takahashi. Critical norm blow-up for a supercritical semilinear heat equation, Mathematical Analysis on Fluid Dynamics and Conservation Laws, Sept. 2022.
• Jin Takahashi. Infinite-time blow-down of singular solutions in the fast diffusion equation, SIAM Conference on Analysis of PDE, Mar. 2022.
• Jin Takahashi. Existence of solutions with moving singularities for a semilinear heat equation with a critical exponent, Seminar on Qualitative Theory of Differential Equations, Mar. 2020.

国内会議発表 (査読なし・不明)

• 高橋仁. Sobolev優臨界な半線形熱方程式における臨界ノルム爆発について, 九州関数方程式セミナー, May 2024.
• 高橋仁. Sobolev優臨界な半線形熱方程式における臨界ノルム爆発について, 東北大学応用数理解析セミナー, June 2023.
• 高橋 仁. Blow-up of the critical norm for a supercritical semilinear heat equation, 浜松PDEセミナー, Mar. 2023.
• 高橋仁. Sobolev優臨界な藤田型方程式における臨界ノルム爆発について, 発展方程式における形状解析と漸近解析, Aug. 2022.
• 高橋仁. Fast diffusion方程式における特異解の無限時間blow-downについて, 神戸大学解析セミナー, Nov. 2021.
• 高橋仁. Existence of solutions with moving singularities for a semilinear heat equation with a critical exponent（日本語講演）, 京都大学NLPDEセミナー, June 2021.
• 高橋仁. Hardy parabolic equationの時間局所可解性について, 応用解析研究会, Mar. 2021.
• 高橋仁. ある臨界指数を持つ半線形熱方程式に対する動的特異点を持つ解の存在について, 広島数理解析セミナー, Jan. 2021.
• 高橋仁. ある臨界指数を持つ半線形熱方程式における動的特異点を持つ解の存在について, 九州関数方程式セミナー, Dec. 2020.
• 高橋仁. ある臨界指数を持つ藤田型方程式に対する動的特異点を持つ解の存在について, 鳥取PDE研究集会, Nov. 2020.
• 高橋仁. $u_t-¥Delta u=u^¥frac{N}{N-2}$に対する動的特異点を持つ解の構成, 楕円型・放物型方程式の集いの会, Aug. 2020.
• 高橋仁. 非斉次半線形熱方程式のシャープな可解性条件について, Elliptic & Parabolic セミナー, Aug. 2020.

その他の論文・著書など

• Jin Takahashi. Review of "Fujita type results for a quasilinear parabolic inequality of Hardy-Hénon type with time forcing terms", Math reviews, Mar. 2024.
• Jin Takahashi. Review of "Asymptotic behavior of solutions to coupled porous medium systems with boundary degeneracy", Math reviews, Aug. 2023.
• Jin Takahashi. Review of "Harnack's inequality for singular parabolic equations with generalized Orlicz growth under the non-logarithmic Zhikov's condition", Math reviews, Oct. 2022.
• Jin Takahashi. Review of "ASYMPTOTIC BEHAVIOR OF SOLUTIONS TO POROUS MEDIUM EQUATIONS WITH BOUNDARY DEGENERACY", Math reviews, June 2022.

学位論文

• Time-dependent singularities in semilinear heat equations,  Summary,  博士（理学）,  Tokyo Institute of Technology,  2016/09/20,   
• Time-dependent singularities in semilinear heat equations,  Exam Summary,  博士（理学）,  Tokyo Institute of Technology,  2016/09/20,   
• Time-dependent singularities in semilinear heat equations,  Outline,  博士（理学）,  Tokyo Institute of Technology,  2016/09/20,   
• Time-dependent singularities in semilinear heat equations,  Thesis,  博士（理学）,  Tokyo Institute of Technology,  2016/09/20, 

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