Affiliation:
1. Universidade Federal de Itajubá ‐ IMC Itajubá M.G. Brazil
2. Universidade Tecnológica Federal do Paraná Pato Branco P.R. Brazil
Abstract
In this paper, we consider an inhomogeneous Allen–Cahn problem
where
(
) is a bounded set with smooth boundary and
is a non‐negative Lipschitz‐continuous function in
. Let
be an
‐dimensional hypersurface that divides
into two disjoints components
(
) such that
on
and
in
. Using the variational concept of
‐convergence, we prove the existence of stable stationary solutions developing a transition layer on
as
.
Funder
Conselho Nacional de Desenvolvimento Científico e Tecnológico
Fundação de Amparo à Pesquisa do Estado de Minas Gerais
Subject
General Engineering,General Mathematics