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