报告人:
董昭
报告人单位:
中国科学院数学与系统科学研究院
时间:
14:30-15:30, April 28(Wednesday), 2021
地点:
腾讯会议ID200 874 419
开始时间:
报告人简介:
研究员
年:
日月:
We consider the large time behavior of strong solutions to a kind of stochastic Burgers equation, where the positionxis 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.