We consider a generalisation of the Cahn–Hilliard equation that incorporates an elastic energy density which, being quasiconvex, incorporates microstructure formation on smaller length scales. We prove global existence of weak solutions in certain microstructural regimes in (one and) two dimensions and present sufficient conditions for uniqueness. Preliminary numerical computations to illustrate some characteristic properties of the solutions are presented and compared to earlier Cahn–Hilliard models with elasticity.
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Thomas Blesgen, Isaac Vikram Chenchiah, A generalized Cahn–Hilliard equation incorporating geometrically linear elasticity. Interfaces Free Bound. 13 (2011), no. 1, pp. 1–27