caa a22 4500 467891486 CHVBK 20180406152750.0 cr unu---uuuuu 170328e20060801xx s 000 0 eng 10.1007/s10955-005-8075-x doi (NATIONALLICENCE)springer-10.1007/s10955-005-8075-x From Reactive Boltzmann Equations to Reaction-Diffusion Systems [Elektronische Daten] [M. Bisi, L. Desvillettes] We consider the reactive Boltzmann equations for a mixture of different species of molecules, including a fixed background. We propose a scaling in which the collisions involving this background are predominant, while the inelastic (reactive) binary collisions are very rare. We show that, at the formal level, the solutions of the Boltzmann equations converge toward the solutions of a reaction-diffusion system. The coefficients of this system can be expressed in terms of the cross sections of the Boltzmann kernels. We discuss various possible physical settings (gases having internal energy, presence of a boundary, etc.), and present one rigorous mathematical proof in a simplified situation (for which the existence of strong solutions to the Boltzmann equation is known). Springer Science + Business Media, Inc., 2006 reaction-diffusion nationallicence Boltzmann equation nationallicence diffusion approximation nationallicence Bisi M. Dipartimento di Matematica, Università di Parma, Parco Area delle Scienze 53/A, 43100, Parma aut Desvillettes L. CMLA, ENS de Cachan, UMR 8536 du CNRS, 61 Av. du Pdt. Wilson, 94235, Cachan Cedex aut Journal of Statistical Physics Kluwer Academic Publishers-Plenum Publishers; http://www.springer-ny.com 124/2-4(2006-08-01), 881-912 0022-4715 124:2-4<881 2006 124 10955 https://doi.org/10.1007/s10955-005-8075-x text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10955-005-8075-x text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Bisi M. Dipartimento di Matematica, Università di Parma, Parco Area delle Scienze 53/A, 43100, Parma aut NATIONALLICENCE 700 1- Desvillettes L. CMLA, ENS de Cachan, UMR 8536 du CNRS, 61 Av. du Pdt. Wilson, 94235, Cachan Cedex aut NATIONALLICENCE 773 0- Journal of Statistical Physics Kluwer Academic Publishers-Plenum Publishers; http://www.springer-ny.com 124/2-4(2006-08-01), 881-912 0022-4715 124:2-4<881 2006 124 10955 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer