TRIPLE JUNCTION SOLUTIONS FOR A SINGULARLY PERTURBED NEUMANN PROBLEM
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Date
2011
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SIAM PUBLICATIONS
Abstract
We consider the singularly perturbed Neumann problem epsilon(2)Delta u - u + up = 0, u > 0 in Omega, partial derivative u/partial derivative v = 0 on partial derivative Omega, where p > 1 and Omega is a smooth and bounded domain in R-2. We construct a class of solutions which consist of large number of spikes concentrated on three line segments with a common endpoint which intersect partial derivative Omega orthogonally.
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Keywords
triple junctions, singularly perturbed problems, finite-dimensional reduction, BOUNDARY PEAK SOLUTIONS, CAHN-HILLIARD EQUATION, LEAST-ENERGY SOLUTIONS, SPIKE-LAYER SOLUTIONS, STATIONARY SOLUTIONS, MULTIPEAK SOLUTIONS, ELLIPTIC-EQUATIONS, LOCAL MINIMIZERS, INTERIOR, SYSTEM