报告人：耿世锋 (湘潭大学)

时间：2024年06月15日 10：00-

地址：理科楼LA103

摘要：In this talk, we study the compressible Euler equations with time-dependent damping $-\frac{1}{(1+t)^{\lambda}}\rho u$. We first artfully construct the asymptotic profile, a special linear wave equation with time-dependent damping in the critical case $\lambda=1$, Then we rigorously prove that the solutions time-asymptotically converge to the linear wave equation with critical time-depending damping. We propose a time asymptotic expansion around the self-similar solution of the generalized porous media equation (GPME) and rigorously justify this expansion as $\lambda \in (\frac17,1)$. In other word, instead of the self-similar solution of GPME, the expansion is the best asymptotic profile of the solution to the compressible Euler equations with time-dependent damping.

简介：耿世锋，湘潭大学教授、博士生导师。湖南省“芙蓉学者奖励计划”青年学者，湘潭大学韶峰学者学术骨干，数学与应用数学系主任。博士毕业于中国科学院武汉物理与数学研究所，研究方向为非线性偏微分方程，主要从事可压缩Euler方程组以及相关的流体力学方程的研究工作，已在SIAM J. Math. Anal., Comm. Partial Differential Equations, J. Differential Equations等国内外重要学术刊物上发表多篇学术论文。

邀请人：穆春来   王华桥

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