Geodesic
A generalized Cahn–Hilliard equation incorporating geometrically linear elasticity
Thomas Blesgen1 ; Isaac Vikram Chenchiah2
1Max-Planck-Institut für Mathematik in den Naturwissenschaften, Leipzig, Germany
2University of Bristol, United Kingdom
Interfaces and free boundaries, Tome 13 (2011) no. 1, pp. 1-27

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DOI

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.
DOI : 10.4171/ifb/246
Classification : 35-XX, 65-XX, 74-XX, 00-XX
Mots-clés : Cahn–Hilliard equation, coarsening, elasticity

Thomas Blesgen  1   ; Isaac Vikram Chenchiah  2

1 Max-Planck-Institut für Mathematik in den Naturwissenschaften, Leipzig, Germany
2 University of Bristol, United Kingdom 
Thomas Blesgen; Isaac Vikram Chenchiah. A generalized Cahn–Hilliard equation incorporating geometrically linear elasticity. Interfaces and free boundaries, Tome 13 (2011) no. 1, pp. 1-27. doi: 10.4171/ifb/246
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