北航数学论坛学术报告

——Stability of rarefaction wave for stochastic Burgers equation

董昭

（中国科学院数学与系统科学研究院研究员）

报告时间：2020年11月05日(星期四)下午16：30-17：30

报告地点：沙河校区主楼E-404

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 datau_0(x) satisfies limx→±∞u_0(x) =u± andu_<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.

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，特别是随机流体力学方程。 在国际期刊发表论文60余篇。主持和参加国家自然科学基金委项目多项，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。曾多次出访美国、英国、法国、德国、俄罗斯、日本等多个国家进行合作研究。任best365网页兼职博导，中国科学院大学岗位教授， 数学通讯和应用概率统计编委。

邀请人：韩德仁