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On Quasilinear Parabolic Evolution Equations In Weighted Lp-Spaces Ii, Jeremy Lecrone, Mathias Wilke, Jan Prüss
On Quasilinear Parabolic Evolution Equations In Weighted Lp-Spaces Ii, Jeremy Lecrone, Mathias Wilke, Jan Prüss
Department of Math & Statistics Faculty Publications
Our study of abstract quasi-linear parabolic problems in time-weighted L_p-spaces, begun in 2010, is extended in this paper to include singular lower order terms, while keeping low initial regularity. The results are applied to reaction-diffusion problems, including Maxwell-Stefan diffusion, and to geometric evolution equations like the surface-diffusion flow or the Willmore flow. The method presented here will be applicable to other parabolic systems, including free boundary problems.