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Article Dans Une Revue Advances in Nonlinear Analysis Année : 2017

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

Imran Biswas
  • Fonction : Auteur
Ananta Majee
  • Fonction : Auteur

Résumé

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.

Dates et versions

hal-04312918 , version 1 (28-11-2023)

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Imran Biswas, Ananta Majee, Guy Vallet. On the Cauchy problem of a degenerate parabolic-hyperbolic PDE with Lévy noise. Advances in Nonlinear Analysis, 2017, 8 (1), pp.809-844. ⟨10.1515/anona-2017-0113⟩. ⟨hal-04312918⟩
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