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Some models of Cahn-Hilliard equations in nonisotropic media. (English) Zbl 0965.35170

The author considers a counterpart of the Cahn-Hillard equation \(\rho _t = \nabla (f(\rho)- \alpha \Delta \rho) \) in a class of periodic generalized functions. The existence and uniqueness of the solutions to the initial value problem is discussed. The existence of finite-dimensional attractors is obtained.

MSC:

35Q72 Other PDE from mechanics (MSC2000)
37L30 Attractors and their dimensions, Lyapunov exponents for infinite-dimensional dissipative dynamical systems
35B41 Attractors
35K90 Abstract parabolic equations
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