报告题目：Existence of solutions to a fractional semilinear heat equation in uniformly local weak Zygmund type spaces

报告人：Tatsuki Kawakami教授，Ryukoku University

报告时间：2024年11月6日（周三）14:30

会议地点：20-200

摘要：The study of the solvability of the Cauchy problem for semilinear (fractional) heat equations is divided into the three cases with respect to the nonlinear exponent: $1<p<p_\theta$ (subcritical case), $p>p_\theta$ (supercritical case), and  $p=p_\theta$ (critical case). In this talk we introduce uniformly local weak Zygmund type spaces, and obtain an optimal sufficient condition for the existence of solutions to the critical fractional semilinear heat equation. This talk is based on several joint works with Norisuke Ioku (Tohoku Univ.), Ryo Takada (Univ. of Tokyo), and Kazuhiro Ishige (Univ. of Tokyo).

报告人简介：Tatsuki Kawakami(川上 竜樹)，日本Ryukoku University(龍谷大学)教授，于日本Tohoku University(東北大学)获得博士学位，研究方向为偏微分方程、分数阶扩散系统、动力学边值问题等，其成果发表在J. Math. Pures Appl.、Ann. Inst. H. Poincaré Anal. Non Linéaire、Calc. Var. Partial Differential Equations、Anal. PDE、J. Differential Equations等国际重要期刊上。