SHADOWING MATCHING ERRORS FOR WAVE-FRONT-LIKE SOLUTIONS

Consider a singularly perturbed system epsilon u(t) = epsilon(2)u(xx) + f(u, x, epsilon), u is an element of R(n), x is an element of R, t g reater than or equal to 0. Assume that the system has a sequence of re gular and internal layers occurring alternatively along the x directio n. These ''multiple wave'' solutions can formally be constructed by ma tched asymptotic expansions. To obtain a genuine solution, we derive a Spatial Shadowing Lemma which assures the existence of an exact solut ion that is near the formal asymptotic series provided (1) the residua l errors are small in all the layers, and (2) the matching errors are small along the lateral boundaries of the adjacent layers. The method should work on some other systems like epsilon u(t) = -(- epsilon(2)D( xx))(m) u + .... (C) 1996 Academic Press, Inc.