On the Cauchy problem of a degenerate parabolic-hyperbolic PDE with Lévy noise

Advances in Nonlinear Analysis

article

Imran H. Biswas¹  Ananta K. Majee²  Guy Vallet³ 

[1] Centre for Applicable Mathematics, Tata Institute of Fundamental Research, GKVK Post Office;Mathematisches Institut, Universität Tübingen;Université de Pau & Pays de l’Adour – LMAP UMR – CNRS 5142

关键词: Stochastic PDEs;    Lévy noise;    degenerate parabolic equations;    entropy solutions;    Young measures;   

DOI  :  10.1515/anona-2017-0113

学科分类：社会科学、人文和艺术（综合）

来源: De Gruyter

【 摘 要 】

In this article, we deal with the stochastic perturbation of degenerate parabolic partial differential equations (PDEs). The particular emphasis is on analyzing the effects of a multiplicative Lévy noise on such problems and on establishing a well-posedness theory by developing a suitable weak entropy solution framework. The proof of the existence of a solution is based on the vanishing viscosity technique. The uniqueness of the solution is settled by interpreting Kruzhkov’s doubling technique in the presence of a noise.

【 授权许可】

CC BY