Local and asymptotic analysis of the flow generated by the Cahn–Hilliard–Gurtin equations

We consider the Cahn–Hilliard–Gurtin equation which corresponds, in the isotropic case, to the viscous Cahn–Hilliard equation. The convergence of its solutions toward some steady state is investigated by means of a proper generalization of the Lojasiewicz–Simon Theorem to nongradient-like flows. Furthermore, when the anisotropic coefficients are small, we prove that these steady states can be approximated by the corresponding stationary solutions of the viscous Cahn–Hilliard equation provided that the latter are local minimizers of the Ginzburg–Landau free energy. Received: April 26, 2004; revised: February 24, 2005