Classical solvability of 1-D Cahn-Hilliard equation coupled with elasticity

In this paper, we prove the classical solvability of a nonlinear 1-D system of hyperbolic-parabolic type arising as a model of phase separation in deformable binary alloys. The system is governed by the nonstationary elasticity equation coupled with the Cahn-Hilliard equation. The existence proof is based on the application of the Leray-Schauder fixed point theorem and standard energy methods.