Heteroclinic solutions of singular quasilinear bistable equations
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 st...
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| Outros Autores: | , |
| Formato: | article |
| Idioma: | eng |
| Publicado em: |
2017
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| Assuntos: | |
| Texto completo: | http://hdl.handle.net/10400.21/7539 |
| País: | Portugal |
| Oai: | oai:repositorio.ipl.pt:10400.21/7539 |
| Resumo: | 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. |
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