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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 Kruzkov'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.
Behera et al. (Sat,) studied this question.