Abstract In this paper, a class of initial boundary problem of the singular perturbed semi-linear delayed parabolic partial differential equation is discussed. The formal asymptotic expansion of the problem is obtained. The maximum principle of the singular perturbed delayed semi-linear parabolic partial differential equations is proved. Then, the maximum-norm estimation and Schauder estimation for this problem are obtained. By the maximum-norm estimation and Schauder estimation for this problem, the existence and uniqueness of the solution of the problem on the columnar zone is proved, and the uniformly valid estimation of the asymptotic expansion is gained.
BAO Li-ping. The asymptotic solution of a class of singular perturbed semi-linear delayed parabolic partial differential equation. Applied Mathematics A Journal of Chinese Universities, 2016, 31(3): 307-315.
