On a singular heat equation with dynamic boundary conditionsReport as inadecuate



 On a singular heat equation with dynamic boundary conditions


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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.



Author: Giulio Schimperna; Antonio Segatti; Sergey Zelik

Source: https://archive.org/







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