On the loss of compactness in the vectorial heteroclinic connection problem. Issue 3 (22nd March 2016)

• Record Type: Journal Article
• Authors: Katzourakis, Nikos
• Is Part Of: Proceedings. Volume 146:Issue 3(2016)
• Page Start: 595
• Page End: 608
• Publication Date: 2016-03-22
• Subjects: Heteroclinic connection problem, -- loss of compactness, -- phase transitions, -- Hamiltonian system; Primary 34C37, -- 46B50, -- 82B26, -- Secondary 37K05; Mathematics -- Periodicals; 510
• DOI: 10.1017/S0308210515000700
• Languages: English
• ISSNs: 0308-2105

Abstract

Abstract : We give an alternative proof of the theorem of Alikakos and Fusco concerning existence of heteroclinic solutions U : ℝ → ℝ N to the system Here a ± are local minima of a potential W ∈ C 2 (ℝ N ) with W ( a ± ) = 0. This system arises in the theory of phase transitions. Our method is variational but differs from the original artificial constraint method of Alikakos and Fusco and establishes existence by analysing the loss of compactness in minimizing 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.