Work

Cauchy Problem for Singular-Degenerate Porous Medium Type Equations: Well-Posedness and Sobolev Regularity

Year: 2025

Type: article

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 [Formula: see text]-accretive operator theory, kinetic formulations, and Fourier analytic techniques.

Source: SIAM Journal on Mathematical Analysis

DOI: 10.1137/23m1620909

Authors: Nick Lindemulder, Stefanie Sonner

Institution: Radboud University Nijmegen

Language: English

Topic: Nonlinear Partial Differential Equations

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: Nederlandse Organisatie voor Wetenschappelijk Onderzoek

Award: Mathematical analysis of quasilinear reaction-diffusion models for bacterial biofilms