Abstract

In this article we study the existence and profile of high-energy solutions for the phase transition model ?2u? - a(x)W?(u) = 0, in (-1, 1), u?(-1) = u?(1) = 0, with W a double well balanced potential and ? is a small parameter. These solutions will be shown to be highly oscillatory. We will characterize their asymptotic behavior in terms of an envelope function. © 2003 Elsevier Inc. All rights reserved.