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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2408.13530 |
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| _version_ | 1866909294750859264 |
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| author | Behera, Soumya Ranjan Majee, Ananta K |
| author_facet | Behera, Soumya Ranjan Majee, Ananta K |
| contents | 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 Kružkov'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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_13530 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Homogeneous Dirichlet problem for degenerate parabolic-hyperbolic PDE driven by Levy noise Behera, Soumya Ranjan Majee, Ananta K Analysis of PDEs 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 Kružkov'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. |
| title | Homogeneous Dirichlet problem for degenerate parabolic-hyperbolic PDE driven by Levy noise |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2408.13530 |