Global existence of solutions to a nonlocal equation with degenerate anisotropic diffusion
Analysis of PDEs
2024-10-18 v3
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.
Keywords
Cite
@article{arxiv.2406.15318,
title = {Global existence of solutions to a nonlocal equation with degenerate anisotropic diffusion},
author = {Maria Eckardt and Anna Zhigun},
journal= {arXiv preprint arXiv:2406.15318},
year = {2024}
}