Renormalized stochastic entropy solution for degenerate parabolic-hyperbolic equations with Levy noise
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866913478946586624 |
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| author | Behera, Soumya Ranjan Majee, Ananta K |
| author_facet | Behera, Soumya Ranjan Majee, Ananta K |
| contents | 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 Kružkov's doubling the variables technique in the presence of noise. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_13528 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Renormalized stochastic entropy solution for degenerate parabolic-hyperbolic equations with Levy noise Behera, Soumya Ranjan Majee, Ananta K Analysis of PDEs Probability 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 Kružkov's doubling the variables technique in the presence of noise. |
| title | Renormalized stochastic entropy solution for degenerate parabolic-hyperbolic equations with Levy noise |
| topic | Analysis of PDEs Probability |
| url | https://arxiv.org/abs/2408.13528 |