Asymptotics of solutions in an A + B → C reaction-diffusion system

Article Article scientifique Article Asymptotics of solutions in an A + B → C reaction-diffusion system eng 1993 author Schenkel Alain 28886 author Wittwer Peter 26560 author Stubbe Joachim 24127 135-147 10.1016/0167-2789(93)90185-4 0167-2789 http://linkinghub.elsevier.com/retrieve/pii/0167278993901854 We analyze the long time behavior of an initial value problem that models a chemical reaction-diffusion process A + B → C. The problem has previously been studied by Gálfi and Rácz, who predicted the critical indices associated with the reaction by using a scaling ansatz motivated by numerical simulations. In this paper we point out some difficulties which appear in problems of this type due to the non-uniform convergence of the solution towards the scaling limit, and solve them by giving an explicit description of the corrections scaling that have to be concluded to prove bounds on the solution that are uniform in space and time. This allows us to relate rigorously the critical exponents as computed from the scaling ansatz to the exponents of the reaction. Dewey 500.2 37 Département de physique théorique 133 false Physica D: Nonlinear Phenomena 69 1-2 cba140f4-373b-4e8b-91aa-75dd4daaa864 Article (Published version) Restricted Schenkel_PhysicaD_1993069135.pdf 822363 application/pdf restrictedAccess Faculté des sciences / Section de physique / Département de physique théorique

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Asymptotics of solutions in an A + B → C reaction-diffusion system	Physica D: Nonlinear Phenomena			1993	323	0

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Schenkel, Alain