Ž . JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS 199, 349373 1996 ARTICLE NO. 0146 The Fast Reaction Limit for a Reaction-Diffusion System D. Hilhorst Laboratoire d’Analyse Numerique, Batiment 425, CNRS et Uni  ersite Paris-Sud, 91405 ´ ˆ ´ Orsay Cedex, France ´ R. van der Hout Akzo Nobel Central Research, PB 9300, 6800 SB Arnhem, The Netherlands and L. A. Peletier Mathematical Institute, Leiden Uni  ersity, PB 9512, 2300 RA Leiden, The Netherlands Submitted by Barbara Lee Keyfitz Received April 7, 1994 1. INTRODUCTION In this paper we shall be concerned with the reaction-diffusion problem  2  u  u 1.1 Ž .   ku  2  t  x  I Ž.   1.2 Ž . ku  ,   t which originates from the chemical reaction k A  B  C , of a chemical substance A, which reacts with a substrate B. If one assumes that the reaction is governed by mass action kinetics and in addition that 349 0022-247X96 $18.00 Copyright  1996 by Academic Press, Inc. All rights of reproduction in any form reserved.