Abstract: We considered a class of two-dimensional singularly perturbed reaction-diffusion problems with  discontinuous reaction terms. Firstly, using spatial contrastive  structural theory, boundary layer function methods, smooth seaming method, and asymptotic differential inequality methods, we constructed  asymptotic expansion of the problem with solutions for the internal layer and boundary layer up to the n order, where n was an arbitary constant. Secondly, we  proved the existence and local asymptotic stability of the solution with internal layer,  and constructed high-precision asymptotic expansion of the solution. Finally, we applied the obtained theoretical results  to a numerical example.

Key words: singular perturbation, reaction-diffusion equation,  , spatial contrastive structural theory, asymptotic expansion