On a singular heat equation with dynamic boundary conditions

2013/02/20 by Schimperna, Giulio, Segatti, Antonio, Zelik, Sergey
#35K51 #35K55 #35K67 #80A22 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1302.5026

Abstract

In this paper we analyze a nonlinear parabolic equation characterized by a singular diffusion term describing very fast diffusion effects. The equation is settled in a smooth bounded three-dimensional domain and complemented with a general boundary condition of dynamic type. This type of condition prescribes some kind of mass conservation; hence extinction effects are not expected for solutions that emanate from strictly positive initial data. Our main results regard existence of weak solutions, instantaneous regularization properties, long-time behavior, and, under special conditions, uniqueness.

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