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arXiv · 2406.15318

Global existence of solutions to a nonlocal equation with degenerate anisotropic diffusion

Maria Eckardt·Anna Zhigun
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Abstract

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.

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Maria Eckardt, Anna Zhigun. 2024-06-21. Global existence of solutions to a nonlocal equation with degenerate anisotropic diffusion. https://arxiv.org/abs/2406.15318

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