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Advisor(s)
Abstract(s)
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.
Description
Keywords
Mean curvature operator in Lorentz–Minkowski space Free energy functional Phase transition Increasing rearrangement Rigidity Symmetry
Citation
BONHEURE, Denis; COELHO, Maria Isabel Esteves; NYS, Manon - Heteroclinic solutions of singular quasilinear bistable equations. NODEA - Nonlinear Differential Equations and Applications. ISSN 1021-9722. Vol. 24, N.º 1 (2017), pp. 1-29
Publisher
Springer Publishing Company