In this article, we consider the semilinear elliptic problem
in with the Neumann boundary condition. The function is a function satisfying for and . In particular we consider the case on some interval . The function is a positive function satisfying . We investigate an asymptotic profile of the global minimizer corresponding to the energy functional as . We use the variational procedure used in  with a few modifications prompted by the presence of the function .
Submitted August 31, 2005. Published January 11, 2006.
Math Subject Classifications: 35B40, 35J25, 35J55, 35J50, 35K57.
Key Words: Transition layer; Allen-Cahn equation; bistable equation; unbalanced.
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| Hiroshi Matsuzawa |
Numazu National College of Technology
Ooka 3600, Numazu-city, Shizuoka 410-8501, Japan
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