JournalsjemsVol. 8, No. 2pp. 355–373

On the necessity of gaps

  • Hiroshi Matano

    University of Tokyo, Japan

  • Paul H. Rabinowitz

    University of Wisconsin, Madison, United States
On the necessity of gaps cover
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Abstract

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.

Cite this article

Hiroshi Matano, Paul H. Rabinowitz, On the necessity of gaps. J. Eur. Math. Soc. 8 (2006), no. 2, pp. 355–373

DOI 10.4171/JEMS/57