Cauchy problem for singular-degenerate porous medium type equations: well-posedness and Sobolev regularity
Analysis of PDEs
2023-12-05 v1
Abstract
Motivated by models for biofilm growth, we consider Cauchy problems for quasilinear reaction diffusion equations where the diffusion coefficient has a porous medium type degeneracy as well as a singularity. We prove results on the well-posedness and Sobolev regularity of solutions. The proofs are based on m-accretive operator theory, kinetic formulations and Fourier analytic techniques.
Keywords
Cite
@article{arxiv.2312.01863,
title = {Cauchy problem for singular-degenerate porous medium type equations: well-posedness and Sobolev regularity},
author = {Nick Lindemulder and Stefanie Sonner},
journal= {arXiv preprint arXiv:2312.01863},
year = {2023}
}