On a singular heat equation with dynamic boundary conditions

Giulio Schimperna; Antonio Segatti; Sergey Zelik

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arXiv · 1302.5026

On a singular heat equation with dynamic boundary conditions

Giulio Schimperna·Antonio Segatti·Sergey Zelik

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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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Giulio Schimperna, Antonio Segatti, Sergey Zelik. 2013-02-20. On a singular heat equation with dynamic boundary conditions. https://arxiv.org/abs/1302.5026

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