On the Loss of Compactness in the Vectorial Heteroclinic Connection Problem

2008/04/17 by Nikos Katzourakis, Katzourakis, Nikos
Computer Science · Engineering · Mathematics · #Contact Mechanics and Variational Inequalities #Elasticity and Material Modeling #Tribology and Lubrication Engineering #math.AP #math.CA

paper · pdf · doi:10.48550/arxiv.0804.2692

Journal: Proc. Royal Soc. Edinburgh, revised, 13 pages, 6 figures

arxiv created 2015/04/14 · arxiv updated 2015/04/15

Abstract

We give an alternative proof of the theorem of Alikakos-Fusco [AF] concerning existence of heteroclinic solutions to a Hamiltonian ODE system on the whole real line which arises in the theory of phase transitions. Our method is variational but differs from the original artificial constraint method of [AF] and establishes existence by analysing the loss of compactness in minimising sequences of the action in the appropriate functional space. Our assumptions are slightly different from those considered previously and also imply a priori estimates for the solution.

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