Global existence of solutions to a nonlocal equation with degenerate anisotropic diffusion
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866910654537924608 |
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| author | Eckardt, Maria Zhigun, Anna |
| author_facet | Eckardt, Maria Zhigun, Anna |
| contents | Global existence of very weak solutions to a non-local diffusion-advection-reaction equation is established under no-flux boundary conditions in higher dimensions. The equation features degenerate myopic diffusion and nonlocal adhesion and is an extension of a mass-conserving model recently derived in arXiv:2308.05676. The admissible degeneracy of the diffusion tensor is characterised in terms of the upper box fractal dimension. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_15318 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Global existence of solutions to a nonlocal equation with degenerate anisotropic diffusion Eckardt, Maria Zhigun, Anna Analysis of PDEs 35K65 35Q92 45K05 92C17 Global existence of very weak solutions to a non-local diffusion-advection-reaction equation is established under no-flux boundary conditions in higher dimensions. The equation features degenerate myopic diffusion and nonlocal adhesion and is an extension of a mass-conserving model recently derived in arXiv:2308.05676. The admissible degeneracy of the diffusion tensor is characterised in terms of the upper box fractal dimension. |
| title | Global existence of solutions to a nonlocal equation with degenerate anisotropic diffusion |
| topic | Analysis of PDEs 35K65 35Q92 45K05 92C17 |
| url | https://arxiv.org/abs/2406.15318 |