On the local well-posedness of randomly forced reaction-diffusion equations with $L^2$ initial data and a superlinear reaction term
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| Format: | Preprint |
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2025
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| _version_ | 1866918407234912256 |
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| author | Foondun, Mohammud Khoshnevisan, Davar Nualart, Eulalia |
| author_facet | Foondun, Mohammud Khoshnevisan, Davar Nualart, Eulalia |
| contents | We consider a parabolic stochastic partial differential equation (SPDE) on $[0\,,1]$ that is forced with multiplicative space-time white noise with a bounded and Lipschitz diffusion coefficient and a drift coefficient that is locally Lipschitz and satisfies an $L\log L$ growth condition. We prove that the SPDE is well posed when the initial data is in $L^2[0\,,1]$. This solves a strong form of an open problem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_00214 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the local well-posedness of randomly forced reaction-diffusion equations with $L^2$ initial data and a superlinear reaction term Foondun, Mohammud Khoshnevisan, Davar Nualart, Eulalia Probability We consider a parabolic stochastic partial differential equation (SPDE) on $[0\,,1]$ that is forced with multiplicative space-time white noise with a bounded and Lipschitz diffusion coefficient and a drift coefficient that is locally Lipschitz and satisfies an $L\log L$ growth condition. We prove that the SPDE is well posed when the initial data is in $L^2[0\,,1]$. This solves a strong form of an open problem. |
| title | On the local well-posedness of randomly forced reaction-diffusion equations with $L^2$ initial data and a superlinear reaction term |
| topic | Probability |
| url | https://arxiv.org/abs/2510.00214 |