Abstract: A class of singular perturbation problem of the reaction diffusion initial value equation was studied. Under suitable conditions, the generalized outer solution to reduced problems was considered. Then the interior shock and boundary layer correction solutions to the original problem were constructed by using the theory of generalized functions. Finally, using the fixed point theorem, the uniform validity of the generalized asymptotic solution with interior shock and initial layers was proved.

Key words: singular perturbation, nonlinear equation, shock layer