Homogeneous Dirichlet problem for degenerate parabolic-hyperbolic PDE driven by Levy noise
Analysis of PDEs
2024-08-27 v1
Abstract
In this article, we study the homogeneous Dirichlet problem for a degenerate parabolic-hyperbolic PDE perturbed by Levy noise. In particular, we develop the well-posedness theory of entropy solution based on the Kru\v{z}kov's semi-entropy formulation. In comparison to the pioneered work by Bauzet et al. (J. Funct. Anal. 266, (2014), 2503-2545), concerning the existence and uniqueness of entropy solution for the Dirichlet problem for conservation laws driven by Brownian noise, our present analysis involves a simpler approach to obtain the global Kato's inequality.
Cite
@article{arxiv.2408.13530,
title = {Homogeneous Dirichlet problem for degenerate parabolic-hyperbolic PDE driven by Levy noise},
author = {Soumya Ranjan Behera and Ananta K Majee},
journal= {arXiv preprint arXiv:2408.13530},
year = {2024}
}