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.


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