Issue |
ESAIM: COCV
Volume 8, 2002
A tribute to JL Lions
|
|
---|---|---|
Page(s) | 965 - 1005 | |
DOI | https://doi.org/10.1051/cocv:2002039 | |
Published online | 15 August 2002 |
Asymmetric heteroclinic double layers
MAPLY,
CNRS et Université Claude Bernard,
69622 Villeurbanne Cedex,
France; schatz@numerix.univ-lyon1.fr.
Received:
14
January
2002
Let W be a non-negative function of class C3 from to
, which vanishes exactly at two points a and b. Let
S1(a, b) be the set of functions of a real variable which tend
to a at -∞
and to b at +∞ and whose one dimensional energy
is finite.
Assume that there exist two isolated minimizers z+ and z-
of the energy E1
over S1(a, b). Under a mild coercivity condition on the
potential W and a generic spectral condition on the linearization
of the
one-dimensional Euler–Lagrange operator at z+ and z-, it is
possible to prove that there exists a function u
from
to itself which satisfies the equation
and the boundary conditions
The above convergences are exponentially fast; the numbers m+
and m- are unknowns of the problem.
Mathematics Subject Classification: 35J50 / 35J60 / 35B40 / 35A15 / 35Q99
Key words: Heteroclinic connections / Ginzburg–Landau / elliptic systems in unbounded domains / non convex optimization.
© EDP Sciences, SMAI, 2002
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.