A generalized Cahn–Hilliard equation incorporating geometrically linear elasticity | Zendy

Thomas Blesgen | Zendy; Isaac V. Chenchiah | Zendy

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A generalized Cahn–Hilliard equation incorporating geometrically linear elasticity

Author(s) -

Thomas Blesgen,

Isaac V. Chenchiah

Publication year - 2011

Publication title -

interfaces and free boundaries mathematical analysis computation and applications

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.964

H-Index - 39

eISSN - 1463-9971

pISSN - 1463-9963

DOI - 10.4171/ifb/246

Subject(s) - cahn–hilliard equation , uniqueness , quasiconvex function , elasticity (physics) , mathematics , computation , linear elasticity , mathematical analysis , statistical physics , partial differential equation , physics , geometry , thermodynamics , finite element method , algorithm , subderivative , convex optimization , regular polygon

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. First numerical computations to illustrate some characteristic properties of the solutions are presented and compared to earlier Cahn-Hilliard models with elasticity. 2010 Mathematics Subject Classification: Primary 35K55, 74B99, 74Q15; Secondary 35K40, 65M60, 74N99.

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