概率统计系列讲座三：
报告题目【Stability of Rarefaction Wave for Stochastic Burgers Equation】
时间：2020年9月9日 (星期三) 14:30
地点：腾讯会议511 3889 6273
主讲：中科院数学与系统科学研究院应用数学研究所，董昭研究员
主办：数学与信息学院
参加对象：统计系老师与学生
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 two dimensional viscous conservation law with stochastic force. This is joint work with Feimin Huang, Houqi Su.