Stochastic non-isotropic degenerate parabolic-hyperbolic equations

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:127

Article

Gess, Benjamin¹  Souganidis, Panagiotis E.² 

[1] Max Planck Inst Math Sci, D-04103 Leipzig, Germany

[2] Univ Chicago, Dept Math, Chicago, IL 60637 USA

关键词: Stochastic scalar conservation laws;    Parabolic-hyperbolic equations;    Averaging lemma;    Invariant measure;    Random dynamical systems;    Random attractor;   

DOI  :  10.1016/j.spa.2017.01.005

来源: Elsevier

【 摘 要 】

We introduce the notion of pathwise entropy solutions for a class of degenerate parabolic hyperbolic equations with non-isotropic nonlinearity and fluxes with rough time dependence and prove their well-posedness. In the case of Brownian noise and periodic boundary conditions, we prove that the path wise entropy solutions converge to their spatial average and provide an estimate on the rate of convergence. The third main result of the paper is a new regularization result in the spirit of averaging lemmata. This work extends both the framework of pathwise entropy solutions for stochastic scalar conservation laws introduced by Lions, Perthame and Souganidis and the analysis of the long time behavior of stochastic scalar conservation laws by the authors to a new class of equations. (C) 2017 Elsevier B.V. All rights reserved.

【 授权许可】

Free