Quasi-steady-state approximation for a reaction–diffusion system with fast intermediate

We consider a prototype reaction–diffusion system which models a network of two consecutive reactions in which chemical components A and B form an intermediate C which decays into two products P and Q. Such a situation often occurs in applications and in the typical case when the intermediate is highly reactive, the species C is eliminated from the system by means of a quasi-steady-state approximation. In this paper, we prove the convergence of the solutions in L2, as the decay rate of the intermediate tends to infinity, for all bounded initial data, even in the case of initial boundary layers. The limiting system is indeed the one which results from formal application of the QSSA. The proof combines the recent L2-approach to reaction–diffusion systems having at most quadratic reaction terms, with local L∞-bounds which are independent of the decay rate of the intermediate. We also prove existence of global classical solutions to the initial system.