A generalized Cahn–Hilliard equation incorporating geometrically linear elasticity
Thomas BlesgenMax-Planck-Institut für Mathematik in den Naturwissenschaften, Leipzig, Germany
Isaac Vikram ChenchiahUniversity 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.
Cite this article
Thomas Blesgen, Isaac Vikram Chenchiah, A generalized Cahn–Hilliard equation incorporating geometrically linear elasticity. Interfaces Free Bound. 13 (2011), no. 1, pp. 1–27DOI 10.4171/IFB/246