Stability in a semilinear boundary value problem via invariant conefields

[摘要] We give a geometric proof of stability for spatially nonhomogeneous equilibria in the singular perturbation problem u(t) = epsilon(2)u(xx) + f(x, u), t is an element of R+, -1 less than or equal to u less than or equal to 1, with the Neumann boundary conditions on x is an element of [0, 1]. The nonlinearity is of the form f(x, u): = (1 - u(2))(u - c(x)), where c(x) is merely continuous with a finite number of zeros. The strength of the method is in dealing with non-transversal zeros of c, the case escaping the existing techniques of singular perturbations. The approach is also used for showing existence of unstable equilibria with one transition layer. (C) 1997 Academic Press.

[发布日期] 1997-11-20