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arXiv · 2408.13528

Renormalized stochastic entropy solution for degenerate parabolic-hyperbolic equations with Levy noise

Soumya Ranjan Behera·Ananta K Majee
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Abstract

In this article, we establish the well-posedness theory for renormalized entropy solutions of a degenerate parabolic-hyperbolic PDE perturbed by a multiplicative Levy noise with general L1-data on the unbounded domain. By using a suitable approximation procedure based on the vanishing viscosity technique and bounded data, we prove the existence of a renormalized entropy solution to the underlying problem. The uniqueness of the solution is settled by adapting Kru\v{z}kov's doubling the variables technique in the presence of noise.

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Soumya Ranjan Behera, Ananta K Majee. 2024-08-24. Renormalized stochastic entropy solution for degenerate parabolic-hyperbolic equations with Levy noise. https://arxiv.org/abs/2408.13528

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