A Cahn-Hilliard equation with singular diffusion

2012/06/25 by Schimperna, Giulio, Pawlow, Irena · 3 citations
#35A01 #35K35 #35K67 #82D60 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1206.5604

Abstract

In the present work, we address a class of Cahn-Hilliard equations characterized by a singular diffusion term. The problem is a simplified version with constant mobility of the Cahn-Hilliard-de Gennes model of phase separation in binary, incompressible, isothermal mixtures of polymer molecules. It is proved that, for any final time T, the problem admits a unique energy type weak solution, defined over (0,T). For any s > 0 such solution is classical in the sense of belonging to a suitable Hoelder class over (s,T), and enjoys the property of being separated from the singular values corresponding to pure phases.

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