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arXiv · 2312.01863

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

Nick Lindemulder·Stefanie Sonner
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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.

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Nick Lindemulder, Stefanie Sonner. 2023-12-04. Cauchy problem for singular-degenerate porous medium type equations: well-posedness and Sobolev regularity. https://arxiv.org/abs/2312.01863

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