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

Imran H. Biswas, Ananta K. Majee, Guy Vallet
2017 Advances in Nonlinear Analysis  
AbstractIn 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
more » ... zhkov's doubling technique in the presence of a noise.
doi:10.1515/anona-2017-0113 fatcat:mv2h3iucujep7oqmnie2qpeljy