Heteroclinic solutions of singular quasilinear bistable equations

• Autor(a) principal: Bonheure, Denis
• Data de Publicação: 2017
• Outros Autores: Coelho, Maria Isabel Esteves, NYS, Manon
• Tipo de documento: Artigo
• Idioma: eng
• Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
• Texto Completo: http://hdl.handle.net/10400.21/7539
• topic: Mean curvature operator in Lorentz–Minkowski space; Free energy functional; Phase transition; Increasing rearrangement; Rigidity; Symmetry

In this note we consider the action functional integral(R x ω) (1-root [1-(|∇u|)^2] + W(u) dx¯), where W is a double well potential and ω is a bounded domain of RN-1. We prove existence, one-dimensionality and uniqueness (up to translations) of a smooth minimizing phase transition between the two stable states u=-1 and u=1. The question of existence of at least one minimal heteroctinic connection for the non-autonomous model integral(R) (1-root [1-(|u’|)^2]+a(t)W(u))dt is also addressed. For this functional, we look for the possible assumptions on a(t) ensuring the existence of a minimizer.