Revista Matemática Iberoamericana


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Volume 18, Issue 3, 2002, pp. 731–745
DOI: 10.4171/RMI/334

Published online: 2002-12-31

Global existence for the discrete diffusive coagulation-fragmentation equations in $L^1$

Philippe Laurençot[1] and Stéphane Mischler[2]

(1) Université de Toulouse, Toulouse, France
(2) Université de Paris-Dauphine, Paris, France

Existence of global weak solutions to the discrete coagulation-fragmentation equations with diffusion is proved under general assumptions on the coagulation and fragmentation coefficients. Unlike previous works requiring $L^\infty$-estimates, an $L^1$-approach is developed here which relies on weak and strong compactness methods in $L^1$.

Keywords: Cluster growth, coalescence, breakage, infinite system of reaction-diffusion equations, existence, weak compactness

Laurençot Philippe, Mischler Stéphane: Global existence for the discrete diffusive coagulation-fragmentation equations in $L^1$. Rev. Mat. Iberoam. 18 (2002), 731-745. doi: 10.4171/RMI/334