The Dirichlet problem for stochastic porous medium equations

活动时间:2023-12-26 15:00

活动地点:2号学院楼247教室

主讲人:杜恺

主讲人中文简介:

杜恺,复旦大学上海数学中心长聘副教授、博士生导师;2011年获复旦大学博士学位,曾任职于苏黎世联邦理工学院、澳大利亚卧龙岗大学;主要研究方向包括随机分析、偏微分方程、最优控制、强化学习等,成果发表于PTRF、TAMS、SICON等国际主流期刊;2019年获聘上海市“东方学者”特聘教授,2022年入选国家优秀青年科学基金项目。

活动内容摘要:

Motivated by porous medium equations with randomly perturbed velocity field, this talk considers a class of nonlinear degenerate diffusion equations with nonlinear conservative noise in bounded domains.  The existence, uniqueness and L^1-stability of non-negative entropy solutions under the homogeneous Dirichlet boundary condition are proved. The approach combines Kruzhkov's doubling variables technique with a revised strong entropy condition that is automatically satisfied by the solutions of approximate equations. This talk is based on a recent work with Ruoyang Liu and Yuxing Wang.

主持人:闫理坦