Parabolic problems with slightly superlinear convection terms
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866908681763815424 |
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| author | Achhoud, Fessel |
| author_facet | Achhoud, Fessel |
| contents | In this paper we deal with a non-linear parabolic problem which involving a convection term with super--linear growth, whose model is \[ \frac{\partial u}{\partial t}-÷(\mathcal{M}(x,t)\nabla u)= -÷(u\log (e+|u|)E(x,t))+f(x,t), \] where $\mathcal{M}$ is a bounded measurable matrix, the vector field $E$ and the function $f$ belong to suitable Lebesgue spaces. We prove the existence of a unique bounded and unbounded weak solution. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_00495 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Parabolic problems with slightly superlinear convection terms Achhoud, Fessel Analysis of PDEs In this paper we deal with a non-linear parabolic problem which involving a convection term with super--linear growth, whose model is \[ \frac{\partial u}{\partial t}-÷(\mathcal{M}(x,t)\nabla u)= -÷(u\log (e+|u|)E(x,t))+f(x,t), \] where $\mathcal{M}$ is a bounded measurable matrix, the vector field $E$ and the function $f$ belong to suitable Lebesgue spaces. We prove the existence of a unique bounded and unbounded weak solution. |
| title | Parabolic problems with slightly superlinear convection terms |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2512.00495 |