The Cahn-Hilliard equation for deformable elastic continua. (English) Zbl 0987.35156

Carrive, M.; Miranville, A.; Piétrus, A.

Adv. Math. Sci. Appl. 10, No. 2, 539-569 (2000).

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.

Reviewer: Messoud Efendiev (Berlin)

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

Keywords:

Cahn-Hilliard equation; deformable elastic continuum; variational formulation; existence of weak solutions; uniqueness; existence of attractors