We consider the nonlinear problem of inhomogeneous Allen-Cahn equation epsilon(2)Delta u+V(y)u(1-u(2)) = 0 in Omega, partial derivative u/partial derivative v = 0 on partial derivative Omega, where Q is a bounded domain in R-2 with smooth boundary, E is a small positive parameter, v denotes the unit outward normal of partial derivative Omega, V is a positive smooth function on (Omega) over bar. Let Gamma be a curve intersecting orthogonally with partial derivative Omega at exactly two points and dividing Omega into two parts. Moreover, Gamma satisfies stationary and non-degenerate conditions w...
