Riv. Mat. Univ. Parma, Vol. 4, No. 2, 2013

Laurent Desvillettes and Klemens Fellner

Duality- and entropy methods in coagulation-fragmentation models

Pages: 215-263
Received: 12 April 2013   
Accepted: 7 May 2013
Mathematics Subject Classification (2010): 45K05, 35B40, 35A01, 82D60.

Keywords: Coagulation-fragmentation model, gelation, saturation, duality method, entropy method, global weak solution, large-time-behaviour, fast-reaction limit.

Abstract: This article presents a selected overview of the existence theory and qualitative analysis of coagulation-fragmentation models describing the formation and break-up of clusters/particles/polymers in various applications in physics, chemistry, astronomy and biology. In particular, we shall discuss recent results on spatially inhomogeneous coagulation-fragmentation models, which are obtained by duality methods and/or entropy methods. We shall show how a duality argument provides e.g. global-in-time L2-bounds, while the entropy method implies entropy related a priori estimates and explicit convergence to equilibrium.

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