On the necessity of gaps

• Autores: Hiroshi Matano, Paul H. Rabinowitz
• Localización: Journal of the European Mathematical Society, ISSN 1435-9855, Vol. 8, Nº 2, 2006, págs. 355-373
• Idioma: inglés
• DOI: 10.4171/jems/57
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• Resumen

  • Recent papers have studied the existence of phase transition solutions for model equations of Allen-Cahn type equations. These solutions are either single or multi-transition spatially heteroclinics or homoclinics between simpler equilibrium states. A sufficient condition of 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.