【数学与统计及交叉学科前沿论坛------高端学术讲座第198场】

报告题目：Entire solutions with and without radial symmetry in balanced bistable reaction-diffusion equations

报 告 人：Professor Masaharu Taniguchi  Okayama University

报告时间：8月13日周四9:30-10:30

报告地点：阜成路校区教二302

报告摘要：Let $n\geq 2$ be a given integer. In this talk, I assert that an $(n+1)$-dimensional traveling front converges to an $n$-dimensional entire solution as the speed goes to infinity in a balanced bistable reaction-diffusion equation. As the speed of an $(n+1)$-dimensional axially symmetric or asymmetric traveling front goes to infinity, it converges to an $n$-dimensional radially symmetric or asymmetric entire solution in a balanced bistable reaction diffusion equation, respectively. We conjecture that the radially asymmetric entire solutions obtained in this paper are associated with the ancient solutions called the Angenent ovals in the mean curvature flows.

报告题目：Polyhedral entire solutions in reaction-diffusion equations

报 告 人：Professor Masaharu Taniguchi  Okayama University

报告时间：8月13日周四10:40-11:40

报告地点：阜成路校区教二302

报告摘要：In this talk, I study polyhedral entire solutions to a bistable reaction-diffusion equation in $\mathbb{R}^{n}$. We consider a pyramidal traveling front solution to the same equation in $\mathbb{R}^{n+1}$. As the speed goes to infinity, its projection converges to an $n$-dimensional polyhedral entire solution. Conversely, as the time goes to $-\infty$, an $n$-dimensional polyhedral entire solution gives $n$-dimensional pyramidal traveling front solutions. The result in this paper suggests a correlation between traveling front solutions and entire solutions in general reaction-diffusion equations or systems.

报告人简介：谷口雅治教授是非线性偏微分方程，特别是反应扩散方程领域的国际知名学者。现任日本冈山大学数学系主任。他的研究主要聚焦于反应扩散方程中的波前解（traveling fronts）与整体解（entire solutions）的存在性、稳定性及几何结构，在高维行波解方面做出了一系列有国际影响的工作。相关成果发表在 《Annales de l'Institut Henri Poincaré C, Analyse non linéaire》、《Archive for Rational Mechanics and Analysis》、《Journal of Differential Equations》、《Mathematische Annalen》、《SIAM Journal on Mathematical Analysis》等国际一流期刊上。因其“反应扩散方程高维波前解与整体解的研究”，谷口雅治教授于 2025年荣获日本数学会分析学奖（MSJ Analysis Prize），这是日本分析方向最重要的学术奖项之一。谷口雅治教授长期致力于学术服务，目前担任《Journal of Differential Equations》、《Discrete and Continuous Dynamical Systems》等国际著名期刊的编委。