Abstract: A class of generalized singular perturbation initial boundary value problem for the reaction diffusion equation is studied. Firstly, the outer solution to original problem is obtained. Next, the initial layer and interior shock layer corrective terms for the generalized asymptotic solutions to original problem are constructed by using the theory of generalized functions. Finally, used the fixed point theorem of functional analytic, the uniformly validity of the generalized asymptotic solution is proved. In this paper, the shock wave asymptotic solution possess simple, valid and higher accuracy peculiarity.

Key words: singular perturbation problem, reaction diffusion equation, generalized asymptotic solution