The Cahn-Hilliard-Gurtin system coupled with elasticity. (English) Zbl 1119.35099

Bartkowiak, L.; Pawłow, I.

Control Cybern. 34, No. 4, 1005-1043 (2005).

Summary: The paper concerns the existence of weak solutions to the Cahn-Hilliard-Gurtin system coupled with nonstationary elasticity. The system describes phase separation process in elastically stressed material. It generalizes the Cahn-Hilliard equation by admitting a more general structure and by coupling diffusive and elastic effects. The system is studied with the help of a singularly perturbed problem which has the form of a well-known phase field model coupled with elasticity. The established existence results are restricted to the homogeneous problem with gradient energy tensor and elasticity tensor independent of the order parameter.

MSC:

35Q72	Other PDE from mechanics (MSC2000)
74N25	Transformations involving diffusion in solids
35D05	Existence of generalized solutions of PDE (MSC2000)
74A15	Thermodynamics in solid mechanics

Keywords:

Cahn-Hilliard equation; Curtin’s theory; Galerkin approximation; phase separation; elasticity system