A Cahn-Hilliard equation with singular diffusion

Giulio Schimperna; Irena Pawlow

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arXiv · 1206.5604

A Cahn-Hilliard equation with singular diffusion

Giulio Schimperna·Irena Pawlow

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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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Giulio Schimperna, Irena Pawlow. 2012-06-25. A Cahn-Hilliard equation with singular diffusion. https://arxiv.org/abs/1206.5604

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