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, < i> Strong solvability of 3-D Cahn-Hilliard system in elastic solids< /i> , Math. Methods
Appl. Sci.].