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<p>In this article, we study the homogeneous Dirichlet problem for a degenerate parabolic-hyperbolic PDE perturbed by Lévy noise. In particular, we develop the well-posedness theory of entropy solution based on the Kružkov’s semi-entropy formulation. In comparison to the pioneered work by Bauzet et al. [<CitationRef CitationID="CR6">6</CitationRef>, J. Funct. Anal. 266, (2014), 2503-2545], concerning the existence and uniqueness of an 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.</p>

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Homogeneous Dirichlet problem for degenerate parabolic-hyperbolic PDE driven by Lévy noise

  • 期刊论文

  • 发表日期：

    2025年8月5日

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  • Soumya Ranjan Behera,
  • Ananta K. Majee

摘要

In this article, we study the homogeneous Dirichlet problem for a degenerate parabolic-hyperbolic PDE perturbed by Lévy noise. In particular, we develop the well-posedness theory of entropy solution based on the Kružkov’s semi-entropy formulation. In comparison to the pioneered work by Bauzet et al. [6, J. Funct. Anal. 266, (2014), 2503-2545], concerning the existence and uniqueness of an 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.