Stable transition layers in a semilinear diffusion equation with spatial inhomogeneities in N-dimensional domains

We prove existence and establish the asymptotic behavior, as →0, of stable stationary solutions to the equation ut= •[d(x) u]+(1−u2)[u−a(x)], for , where , N 2, with Neumann boundary condition. The function a(x) C0,ν(Ω) satisfies −1