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On the coupled Cahn-Hilliard equations. (English) Zbl 0815.35041
Summary: This paper is concerned with the coupled Cahn-Hilliard equations, which consists of a fourth order quasilinear parabolic equation and a second order quasilinear parabolic equation. The global existence and uniqueness of classical solutions is proved. Results about the asymptotic behavior and about the existence and multiplicity of solutions to the corresponding stationary problem, which is a nonlinear boundary value problem involving nonlocal term and constraints, are also obtained.

MSC:
35K55 Nonlinear parabolic equations
35B40 Asymptotic behavior of solutions to PDEs
35K45 Initial value problems for second-order parabolic systems
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