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

Published 24 Nov 2023 in math.AP | (2311.14522v1)

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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