Article

On the Stationary Cahn–Hilliard Equation: Interior Spike Solutions

Department of Mathematics, Chinese University of Hong Kong, Shatin, Hong Kong, People's Republic of Chinaf1E-mail: .hkf1; Mathematisches Institut, Universität Stuttgart, D-70511, Stuttgart, Germanyf2E-mail: -stuttgart.def2
Journal of Differential Equations DOI:10.1006/jdeq.1998.3479 pp.231-267

ABSTRACT 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 construction uses among others the methods of viscosity solution, weak convergence of measures, and Liapunov–Schmidt reduction.

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Keywords

bounded smooth domain
 
given nondegenerate peak point
 
interior points
 
large class
 
others
 
solutions
 
stationary Cahn–Hilliard equation
 
weak convergence
 
“nondegenerate peak” points
 

Juncheng Wei