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On the stationary Cahn-Hilliard equation: Interior spike solutions. (English) Zbl 0965.35070
Summary: We study solutions of the stationary Cahn-Hilliard equation in a bounded smooth domain which have a spike in the interior. We show that a large class of interior points (the “nondegenerate peak” points) have the following property: There exist such solutions whose spike lies close to a given nondegenerate peak point. Our constrution uses among others the methods of viscosity solution, weak convergence of measures, and Lyapunov-Schmidt reduction.

35J65 Nonlinear boundary value problems for linear elliptic equations
35B25 Singular perturbations in context of PDEs
35J60 Nonlinear elliptic equations
Full Text: DOI
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