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Stationary solutions for the Cahn-Hilliard equation. (English) Zbl 0910.35049

The Cahn-Hilliard equation is an accepted macroscopic field-theoretical model of processes such as phase separation in a binary alloy. This equation is studied in a bounded domain without symmetry assumptions. It is assumed that the mean curvature of the boundary has a nondegenerate critical point. It is shown that there exists a spike-like stationary solution whose global maximum lies on the boundary. The derivation is based on Lyapunov-Schmidt reduction and the Brouwer fixed-point theorem.
Reviewer: I.Ginchev (Varna)

MSC:

35J65 Nonlinear boundary value problems for linear elliptic equations
35B05 Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs
35B40 Asymptotic behavior of solutions to PDEs
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