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arXiv · 1604.05009

On the Cauchy problem of a degenerate parabolic-hyperbolic PDE with L\'{e}vy noise

Imran H. Biswas·Ananta K. Majee·Guy Vallet
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Abstract

In this article we deal with stochastic perturbation of degenerate parabolic partial differential equations (PDEs). The particular emphasise is on analysing the effect of multiplicative L\'{e}vy noise to such problems and establishing wellposedness by developing a suitable weak entropy solution framework. The proof of existence is based on the vanishing viscosity technique. The uniqueness is settled by interpreting Kruzkov's doubling technique in the presence noise.

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Imran H. Biswas, Ananta K. Majee, Guy Vallet. 2016-04-18. On the Cauchy problem of a degenerate parabolic-hyperbolic PDE with L\'{e}vy noise. https://arxiv.org/abs/1604.05009

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