Stability in a Semilinear Boundary Value Problem via Invariant Cone elds
نویسنده
چکیده
We give a geometric proof of stability for spatially nonho-mogeneous equilibria in the singular perturbation problem u t = 2 u xx + f(x; u); t 2 R + ; ?1 u 1, with the Neumann boundary conditions on x 2 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 nite 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.
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