English

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}
}