Abstract: This paper is concerned with an Initial Boundary Value Problem (IBVP) for a strongly coupled semilinear reaction-diffusion system. By using the upper and lower solutions method and Leray-Schauder fixed point theorem and so on, the authors prove the global eaistence and uniqueness of a smooth solution for this IBVP under some appropriate conditions.

Key words: strongly coupled reaction-diffusion system, global smooth solution, upper and lower solutions, Leray-Schauder fixed point theorem