On the Cauchy problem of a degenerate parabolic-hyperbolic PDE with Lévy noise
Imran H. BiswasCentre for Applicable Mathematics, Tata Institute of Fundamental Research, P.O. Box 6503, GKVK Post Office, Bangalore560065, IndiaAnanta K. MajeeMathematisches Institut, Universität Tübingen, Auf der Morgenstelle 10, 72076Tübingen, GermanyVallet GuyUniversité de Pau & Pays de l’Adour– LMAP UMR – CNRS 5142, IPRA BP 1155, 64013Pau Cedex, France
2017en
ABI
Abstract
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.
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