Nonlinear random perturbations of Reaction-Diffusion Equations
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866916803117056000 |
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| author | Cerrai, Sandra Guatteri, Giuseppina Tessitore, Gianmario |
| author_facet | Cerrai, Sandra Guatteri, Giuseppina Tessitore, Gianmario |
| contents | This paper investigates the well-posedness and small-noise asymptotics of a class of stochastic partial differential equations defined on a bounded domain of $\mathbb{R}^d$, where the diffusion coefficient depends nonlinearly and non-locally on the solution through a conditional expectation. The reaction term is assumed to be merely continuous and to satisfy a quasi-dissipativity condition, without requiring any growth bounds or local Lipschitz continuity. This setting introduces significant analytical challenges due to the temporal non-locality and the lack of regularity assumptions. Our results represent a substantial advance in the study of nonlinear stochastic perturbations of SPDEs, extending the framework developed in a previous paper. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_17094 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Nonlinear random perturbations of Reaction-Diffusion Equations Cerrai, Sandra Guatteri, Giuseppina Tessitore, Gianmario Probability This paper investigates the well-posedness and small-noise asymptotics of a class of stochastic partial differential equations defined on a bounded domain of $\mathbb{R}^d$, where the diffusion coefficient depends nonlinearly and non-locally on the solution through a conditional expectation. The reaction term is assumed to be merely continuous and to satisfy a quasi-dissipativity condition, without requiring any growth bounds or local Lipschitz continuity. This setting introduces significant analytical challenges due to the temporal non-locality and the lack of regularity assumptions. Our results represent a substantial advance in the study of nonlinear stochastic perturbations of SPDEs, extending the framework developed in a previous paper. |
| title | Nonlinear random perturbations of Reaction-Diffusion Equations |
| topic | Probability |
| url | https://arxiv.org/abs/2506.17094 |