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Heteroclinic solutions of singular quasilinear bistable equations

par Bonheure, Denis ;Coelho, Maria Isabel ;Nys, Manon
Référence NoDEA. Nonlinear differential equations and applications, 24, 1, 2
Publication Publié, 2017-02

Article révisé par les pairs

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Résumé :

In this note we consider the action functional (Formula presented.) 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 heteroclinic connection for the non-autonomous model (Formula presented.) is also addressed. For this functional, we look for the possible assumptions on a(t) ensuring the existence of a minimizer.