On the $L_1$--stability for parabolic equations with a supercritical drift term
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Acceso en línea: | |
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| _version_ | 1866915007530270720 |
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| author | Glazkov, Mikhail Shilkin, Timofey |
| author_facet | Glazkov, Mikhail Shilkin, Timofey |
| contents | In this paper we investigate the existence, uniqueness and stability of weak solutions of the initial boundary value problem with the Dirichlet boundary conditions for a parabolic equation with a drift $b\in L_2$. We prove $L_1$-stability of solutions with respect to perturbations of the drift $b$ in $L_2$ in the case if the drift satisfies the ``non-spectral'' condition $\operatorname{div} b\le 0$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_03816 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the $L_1$--stability for parabolic equations with a supercritical drift term Glazkov, Mikhail Shilkin, Timofey Analysis of PDEs In this paper we investigate the existence, uniqueness and stability of weak solutions of the initial boundary value problem with the Dirichlet boundary conditions for a parabolic equation with a drift $b\in L_2$. We prove $L_1$-stability of solutions with respect to perturbations of the drift $b$ in $L_2$ in the case if the drift satisfies the ``non-spectral'' condition $\operatorname{div} b\le 0$. |
| title | On the $L_1$--stability for parabolic equations with a supercritical drift term |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2411.03816 |