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)


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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