Numerical Approximation of a Reaction-Diffusion System with Fast Reversible Reaction

The authors consider the finite volume approximation of a reaction-diffusion system with fast reversible reaction. It is deduced from a priori estimates that the approximate solution converges to the weak solution of the reaction-diffusion problem and satisfies estimates which do not depend on the kinetic rate. It follows that the solution converges to the solution of a nonlinear diffusion problem, as the size of the volume elements and the time steps converge to zero while the kinetic rate tends to infinity.

作 者： Robert EYMARD Danielle HILHORST Hideki MURAKAWA Michal OLECH   作者單位： Robert EYMARD(Université Paris-Est, 77454 Marne-la-Vallée Cedex 2, France)

Danielle HILHORST(Laboratoire de Mathématiques, CNRS and Université de Paris-Sud 11, 91405 Orsay Cédex, France)

Hideki MURAKAWA(Graduate School of Science and Engineering for Research, University of Toyama, 3190 Gofuku, Toyama 930-8555, Japan)

Michal OLECH(Instytut Matematyczny Uniwersytctu Wroclawskiego, pl. Grunwaldzki 2/4, 50-384 Wroclaw, Polska; Laboratoire de Mathématiques, CNRS Université de Paris-Sud, 91405 Orsay Cédex, France) 

刊 名： 數學年刊B輯（英文版）  ISTIC SCI 英文刊名： CHINESE ANNALS OF MATHEMATICS,SERIES B  年，卷(期)： 2010 31(5)  分類號： O1  關鍵詞： Instantaneous reaction limit   Mass-action kinetics   Finite volume methods   Convergence of approximate solutions   Discrete a priori estimates   Kolmogorov's theorem