$BV$-Estimates for Non-Linear Parabolic PDE with Linear Drift
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866917187959128064 |
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| author | Erraji, El Mahdi Igbida, Noureddine Karami, Fahd Meskine, Driss |
| author_facet | Erraji, El Mahdi Igbida, Noureddine Karami, Fahd Meskine, Driss |
| contents | In the present work, we establish space Bounded Variation $(BV)$ regularity of the solution for a non-linear parabolic partial differential equations involving a linear drift term. We study the problem in a bounded domain with mixed Dirichlet-Neumann boundary conditions, a general non-linearity and reasonable assumptions on the data. Our results also cover, as a particular case, the linear transport equation in a bounded domain with an outward-pointing drift vector field on the boundary. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_03755 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | $BV$-Estimates for Non-Linear Parabolic PDE with Linear Drift Erraji, El Mahdi Igbida, Noureddine Karami, Fahd Meskine, Driss Analysis of PDEs In the present work, we establish space Bounded Variation $(BV)$ regularity of the solution for a non-linear parabolic partial differential equations involving a linear drift term. We study the problem in a bounded domain with mixed Dirichlet-Neumann boundary conditions, a general non-linearity and reasonable assumptions on the data. Our results also cover, as a particular case, the linear transport equation in a bounded domain with an outward-pointing drift vector field on the boundary. |
| title | $BV$-Estimates for Non-Linear Parabolic PDE with Linear Drift |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2601.03755 |