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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 homoclinics between simpler equilibrium states. A sufficient condition for the construction of the multitransition
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.
Matano, Hiroshi, and Rabinowitz, Paul. "On the necessity of gaps." Journal of the European Mathematical Society 008.2 (2006): 355-373. <http://eudml.org/doc/277395>.
@article{Matano2006, 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 homoclinics between simpler equilibrium states. A sufficient condition for the construction of the multitransition
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.}, author = {Matano, Hiroshi, Rabinowitz, Paul}, journal = {Journal of the European Mathematical Society}, keywords = {Allen–Cahn type equations; phase transition solution; gap conditions}, language = {eng}, number = {2}, pages = {355-373}, publisher = {European Mathematical Society Publishing House}, title = {On the necessity of gaps}, url = {http://eudml.org/doc/277395}, volume = {008}, year = {2006}, }
TY - JOUR AU - Matano, Hiroshi AU - Rabinowitz, Paul TI - On the necessity of gaps JO - Journal of the European Mathematical Society PY - 2006 PB - European Mathematical Society Publishing House VL - 008 IS - 2 SP - 355 EP - 373 AB - 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 homoclinics between simpler equilibrium states. A sufficient condition for the construction of the multitransition
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. LA - eng KW - Allen–Cahn type equations; phase transition solution; gap conditions UR - http://eudml.org/doc/277395 ER -