Well-posedness of the obstacle problem for stochastic nonlinear diffusion equations: an entropy formulation
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866915244290342912 |
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| author | Du, Kai Liu, Ruoyang |
| author_facet | Du, Kai Liu, Ruoyang |
| contents | In this paper, we establish the existence, uniqueness and stability results for the obstacle problem associated with a degenerate nonlinear diffusion equation perturbed by conservative gradient noise. Our approach revolves round introducing a new entropy formulation for stochastic variational inequalities. As a consequence, we obtain a novel well-posedness result for the obstacle problem of deterministic porous medium equations with nonlinear reaction terms. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_02547 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Well-posedness of the obstacle problem for stochastic nonlinear diffusion equations: an entropy formulation Du, Kai Liu, Ruoyang Probability Analysis of PDEs 60H15, 35K86, 35K65, 47J20 In this paper, we establish the existence, uniqueness and stability results for the obstacle problem associated with a degenerate nonlinear diffusion equation perturbed by conservative gradient noise. Our approach revolves round introducing a new entropy formulation for stochastic variational inequalities. As a consequence, we obtain a novel well-posedness result for the obstacle problem of deterministic porous medium equations with nonlinear reaction terms. |
| title | Well-posedness of the obstacle problem for stochastic nonlinear diffusion equations: an entropy formulation |
| topic | Probability Analysis of PDEs 60H15, 35K86, 35K65, 47J20 |
| url | https://arxiv.org/abs/2404.02547 |