报告题目：Stability of rarefaction wave for stochastic Burgers equation

报告时间：2020年5月16日（周六）上午10:40—11:30

报告人：董昭 研究员

报告地点：Zoom云会议（ID：838 4831 5631, 密码：nanxinda60）

报告摘要：The large time behavior of strong solutions to the stochastic Burgers equation is considered in this paper. It is first shown that the unique global strong solution to the one dimensional stochastic Burgers equation time-asymptotically tend to a rarefaction wave provided that the initial data u_0(x) satisfies limx→±∞ u_0(x) = u± and u_< u+, that is, the rarefaction wave is non-linearly stable under white noise perturbation for stochastic Burgers equation. A time-convergence rate is also obtained. Moreover, an important inequality (denoted by Area Inequality) is derived. This inequality plays essential role in the estimates, and may have various applications in the related problems, in particular for the time-decay rate of solutions of both the stochastic and deterministic PDEs. As an application, the stability of planar rarefaction wave is shown stable for a twodimensional viscous conservation law with stochastic force.This is joint work with Feimin Huang, HouqiSu.

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数学与统计学院

2020年5月15日

附：专家简介

董昭，中国科学院数学与系统科学研究院研究员，中国科学院大学岗位教授，北京航空航天大学数学科学院兼职教授，重点项目主持人。1990年北京师范大学数学系获硕士学位，1996年中国科学院应用数学研究所获博士学位。中国概率统计学会常务理事、应用概率统计编委。研究方向是：狄氏型与无穷维随机分析、随机动力系统与随机偏微分方程、软件可靠性。在国内、国外发表论文40 余篇。2006年以来主持5项国家自然基金项目，其中重点项目1项，并参与多项科研项目，如973项目、基金委的创新研究群体等。