Well-posedness results for superlinear Fokker-Planck equations
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866912823933665280 |
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| author | Buccheri, Stefano Farroni, Fernando Zecca, Gabriella |
| author_facet | Buccheri, Stefano Farroni, Fernando Zecca, Gabriella |
| contents | In this manuscript we deal with a class of nonlinear Fokker-Planck equations with the following structure \[ \partial_t u - ÷\big(M\nabla u+ E h(u)\big)=0, \] with $M$ a bounded elliptic matrix, $E$ a vector field in a suitable Lebesgue space, and $h(u)$ featuring a superlinear growth for $u$ large. We provide existence results of $C([0,T),L^1)$ distributional solutions to initial-boundary value problems related to the equation above together with some qualitative properties of solutions. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2601_09341 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Well-posedness results for superlinear Fokker-Planck equations Buccheri, Stefano Farroni, Fernando Zecca, Gabriella Analysis of PDEs In this manuscript we deal with a class of nonlinear Fokker-Planck equations with the following structure \[ \partial_t u - ÷\big(M\nabla u+ E h(u)\big)=0, \] with $M$ a bounded elliptic matrix, $E$ a vector field in a suitable Lebesgue space, and $h(u)$ featuring a superlinear growth for $u$ large. We provide existence results of $C([0,T),L^1)$ distributional solutions to initial-boundary value problems related to the equation above together with some qualitative properties of solutions. |
| title | Well-posedness results for superlinear Fokker-Planck equations |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2601.09341 |