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

Advances in Nonlinear Analysis

Biswas Imran H.¹  Majee Ananta K.²  Vallet Guy³ 

[1] Centre for Applicable Mathematics, Tata Institute of Fundamental Research, P.O. Box 6503, GKVK Post Office, Bangalore560065, India;Mathematisches Institut, Universität Tübingen, Auf der Morgenstelle 10, 72076Tübingen, Germany;Université de Pau & Pays de l’Adour– LMAP UMR – CNRS 5142, IPRA BP 1155, 64013Pau Cedex, France;

关键词: stochastic pdes;    lévy noise;    degenerate parabolic equations;    entropy solutions;    young measures;    35k65 - 60h15;   

DOI  :  10.1515/anona-2017-0113

来源: DOAJ

【 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】

Unknown