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Weak Compactness Techniques and Coagulation Equations

Part of the Lecture Notes in Mathematics book series (LNM,volume 2126)

Abstract

Smoluchowski’s coagulation equation is a mean-field model describing the growth of clusters by successive mergers. Since its derivation in 1916 it has been studied by several authors, using deterministic and stochastic approaches, with a blossoming of results in the last 20 years. In particular, the use of weak L 1-compactness techniques led to a mature theory of weak solutions and the purpose of these notes is to describe the results obtained so far in that direction, as well as the mathematical tools used.

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Acknowledgements

These notes grew out from lectures I gave at the Institut für Angewandte Mathematik, Leibniz Universität Hannover, in September 2008 and at the African Institute for Mathematical Sciences, Muizenberg, in July 2013. I thank Jacek Banasiak, Joachim Escher, Mustapha Mokhtar-Kharroubi, and Christoph Walker for their kind invitations as well as both institutions for their hospitality and support. This work was completed while visiting the Institut Mittag-Leffler, Stockholm.

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Laurençot, P. (2015). Weak Compactness Techniques and Coagulation Equations. In: Banasiak, J., Mokhtar-Kharroubi, M. (eds) Evolutionary Equations with Applications in Natural Sciences. Lecture Notes in Mathematics, vol 2126. Springer, Cham. https://doi.org/10.1007/978-3-319-11322-7_5

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