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- Title
On the necessity of gaps.
- Authors
Matano, Hiroshi; Rabinowitz, Paul H.
- Abstract
Recent papers have studied the existence of phase transition solutions for Allen-Cahn type equations. These solutions are either single or multi-transition spatial heteroclinics or homo- clinics between simpler equilibrium states. A sufficient condition for the construction of the multi- transition solutions is that there are gaps in the ordered set of single transition solutions. In this paper we explore the necessity of these gap conditions.
- Subjects
PHASE transitions; EQUILIBRIUM; RIEMANNIAN manifolds; RIEMANN-Roch theorems; OPERATIONS (Algebraic topology); MATRICES (Mathematics)
- Publication
Journal of the European Mathematical Society (EMS Publishing), 2006, Vol 8, Issue 2, p355
- ISSN
1435-9855
- Publication type
Article
- DOI
10.4171/jems/57