Interfaces and Free Boundaries

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Volume 13, Issue 1, 2011, pp. 1–27
DOI: 10.4171/IFB/246

Published online: 2011-03-22

A generalized Cahn–Hilliard equation incorporating geometrically linear elasticity

Thomas Blesgen[1] and Isaac Vikram Chenchiah[2]

(1) Max-Planck-Institut für Mathematik in den Naturwissenschaften, Leipzig, Germany
(2) University of Bristol, United Kingdom

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.

Keywords: Cahn–Hilliard equation, coarsening, elasticity

Blesgen Thomas, Chenchiah Isaac Vikram: A generalized Cahn–Hilliard equation incorporating geometrically linear elasticity. Interfaces Free Bound. 13 (2011), 1-27. doi: 10.4171/IFB/246