PROBLEMAS NÃO LINEARES DE VALORES NA FRONTEIRA COM O OPERADOR DE CURVATURA PRESCRITA

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Heteroclinic solutions of singular quasilinear bistable equations

Publication . Bonheure, Denis; Coelho, Maria Isabel Esteves; NYS, Manon

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.

2017-02Journal article

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