Strong solvability of 3-D Cahn-Hilliard system in elastic solids

In this paper we prove the existence and uniqueness of a strong solution to a 3-D model of phase separation in elastic solids. The model has the form of an initial-boundary-value problem for a nonlinear coupled system of hyperbolic-parabolic type. The key idea of the proof is based on the analysis of the system once- and twice differentiated with respect to time variable. The paper develops results of the previous work (Top. Meth. Nonlin. Anal., in press).