一、报告题目

Large time behavior of strong solutions for stochastic Burgers equation

二、主讲人

黄飞敏

三、报告时间

2021年9月22日 14：30-15：30

四、报告地点

腾讯会议 ID : 381 986 951

五、摘要

We consider the large time behavior of strong solutions to the stochastic Burgers equation with transportation 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 in 1964. However, the stability of these wave patterns under stochastic perturbation is not known until now. In this paper, we give a definite 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 a joint work with Zhao Dong and Houqi Su.

六、主讲人简介

黄飞敏，中科院数学与系统科学院研究员。国家杰出青年科学基金获得者。曾获得过国家自然科学二等奖、美国工业与应用数学学会杰出论文奖、中国科学院青年科学家奖，中科院数学与系统科学院突出科研成果奖等多项荣誉。担任《数学物理学报》中英文版常务编委、《应用数学学报》中英文版常务编委。研究方向是偏微分方程，在双曲守恒律方程组和粘性守恒律方程组等作出突破性贡献。在Adv. Math., Comm. Math. Phys., Comm.PDEs，Arch. Ration. Mech. Anal.等国际顶尖期刊上发表论文100余篇。

七、主办单位

非线性期望前沿科学中心

数学与交叉科学研究中心