On the necessity of gaps | Zendy

Hiroshi Matano | Zendy; Paul H. Rabinowitz | Zendy

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On the necessity of gaps

Author(s) -

Hiroshi Matano,

Paul H. Rabinowitz

Publication year - 2006

Publication title -

journal of the european mathematical society

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 3.549

H-Index - 64

eISSN - 1435-9863

pISSN - 1435-9855

DOI - 10.4171/jems/57

Subject(s) - mathematics , phase transition , set (abstract data type) , transition (genetics) , type (biology) , mathematical economics , statistical physics , thermodynamics , physics , computer science , ecology , biochemistry , chemistry , biology , gene , programming language

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.

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