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arXiv:2312.01863 [math.AP]AbstractReferencesReviewsResources

Cauchy problem for singular-degenerate porous medium type equations: well-posedness and Sobolev regularity

Nick Lindemulder, Stefanie Sonner

Published 2023-12-04Version 1

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.

Categories: math.AP
Subjects: 35K59, 35K65, 35K67, 35B65, 46E35, 47H05
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