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math.AP2023
Cauchy problem for singular-degenerate porous medium type equations: well-posedness and Sobolev regularity
Nick Lindemulder, Stefanie Sonner
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…
math.AP2023
Well-posedness and qualitative properties of quasilinear degenerate evolution systems
Koondanibha Mitra, Stefanie Sonner
We analyze nonlinear degenerate coupled PDE-PDE and PDE-ODE systems that arise, for example, in the modelling of biofilm growth. One of the equations, describing the evolution of a…