Weak solutions to 3-D Cahn-Hilliard system in elastic solids

Abstract

In this paper we prove the existence and some time regularity of weak solutions to a three-dimensional (3-D) Cahn-Hilliard system coupled with nonstationary elasticity. Such nonlinear parabolic-hyperbolic system arises as a model of phase separation in deformable alloys. The regularity result is based on the analysis of time differentiated problem by means of the Faedo-Galerkin method. The obtained regularity provides a first step to the proof of strong solvability of the problem to be presented in a forthcoming paper [I. Pawłow, W. M. Zajączkowski, Strong solvability of 3-D Cahn–Hilliard system in elastic solids, Math. Methods Appl. Sci.].