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The Cahn-Hilliard equation for deformable elastic continua. (English) Zbl 0987.35156
The authors deal with variants of the Cahn-Hilliard equation which play a crucial role in material sciences. More precisely, they study a model of the Cahn-Hilliard equation in a deformable elastic continuum. The aim is to define boundary conditions that allow a mathematical formulation. To do so, they derive a variational formulation and obtain existence of weak solutions. Having partially results on the uniqueness of weak solutions they finally study the existence of attractors.

MSC:
35Q72 Other PDE from mechanics (MSC2000)
35D05 Existence of generalized solutions of PDE (MSC2000)
35B41 Attractors
37L99 Infinite-dimensional dissipative dynamical systems
74H99 Dynamical problems in solid mechanics
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