On the Loss of Compactness in the Vectorial Heteroclinic Connection\n Problem

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

paper · pdf · doi:10.48550/arxiv.0804.2692

Abstract

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

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