主講人：黃飛敏 中科院數(shù)學(xué)與系統(tǒng)科學(xué)院研究員

時(shí)間：2022年10月31日9：00

地點(diǎn)：騰訊會(huì)議 754 696 999

舉辦單位：數(shù)理學(xué)院

主講人介紹：黃飛敏，中國(guó)科學(xué)院數(shù)學(xué)與系統(tǒng)科學(xué)研究院華羅庚首席研究員，主要研究非線(xiàn)性偏微分方程，曾獲2013年國(guó)家自然科學(xué)獎(jiǎng)二等獎(jiǎng)，國(guó)家杰出青年基金，美國(guó)工業(yè)與應(yīng)用數(shù)學(xué)學(xué)會(huì)杰出論文獎(jiǎng)。

內(nèi)容介紹：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 \cite{Olinik64} 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.