Smooth solutions of degenerate linear parabolic equations and the porous medium equation

Albert Chau; Ben Weinkove

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arXiv · 2311.14522

Smooth solutions of degenerate linear parabolic equations and the porous medium equation

Albert Chau·Ben Weinkove

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Abstract

We prove existence of smooth solutions to linear degenerate parabolic equations on bounded domains assuming a structure condition of Fichera. We use this to give a proof of a smooth short time existence result for the porous medium equation $u_t = \Delta u^m$ for $1<m\le 2$.

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Albert Chau, Ben Weinkove. 2023-11-24. Smooth solutions of degenerate linear parabolic equations and the porous medium equation. https://arxiv.org/abs/2311.14522

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