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The formation of multiple wave fronts is important in applications of singularly perturbed parabolic systems. These solutions can be effectively constructed by formal asymptotic methods. When truncated to a certain order in e, they become formal approximations of solutions to the given system. The precision of a formal approximation is judged by the smallness of the residual error in each regular and singular layer and the jump error between adjacent layers.

Local and Global Existence of Multiple Waves Near Formal Approximations