报告题目：Large time behavior of strong solutions for stochastic Burgers equation

报告人：董昭 （中国科学院大学）

报告时间：2021年5月17日上午10:00-11:00

报告地点：数学院145报告厅

报告摘要：We consider the large time behavior of strong solutions to a kind of stochastic Burgers equation, where the position x is perturbed by a Brownian noise. It is well known that both the rarefaction wave and viscous shock wave are time-asymptotically stable for deterministic Burgers equation since the pioneer work of A. Ilin and O. Oleinik [20] in 1964. However, the stability of these wave patterns under stochastic perturbation is not known until now. In this paper, we give a defifinite answer to the stability problem of the rarefaction and viscous shock waves for the 1-d stochastic Burgers equation. That is, the rarefaction wave is still stable under white noise perturbation and the viscous shock is not stable yet. Moreover, a time-convergence rate toward the rarefaction wave is obtained. To get the desired decay rate, an important inequality (denoted by Area Inequality) is derived. This inequality plays essential role in the proof, and may have applications in the related problems for both the stochastic and deterministic PDEs.

This is joint work with Feimin Huang and Houqi Su.

报告人简介：董昭研究员1996年博士毕业于中科院应用数学研究所。主要从事狄氏型与马氏过程、随机过程、随机（偏）微分方程理论研究，特别是在随机流体力学和多遍历态的随机动力系统有比较深入的研究。在国际期刊发表论文50余篇。主持国家自然科学基金委重点项目一项、面上项目两项，参加重点和面上多项，是973项目和基金委创新研究群体的主要成员。和他人合作获得教育部自然科学二等奖。任北京航空航天大学兼职博导，中国科学院大学岗位教授。