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Mathematical Aspects of Coagulation-Fragmentation Equations

  • F. P. da CostaEmail author
Conference paper
Part of the CIM Series in Mathematical Sciences book series (CIMSMS, volume 2)

Abstract

We give an overview of the mathematical literature on the coagulation-like equations, from an analytic deterministic perspective. In Sect. 1 we present the coagulation type equations more commonly encountered in the scientific and mathematical literature and provide a brief historical overview of relevant works. In Sect. 2 we present results about existence and uniqueness of solutions in some of those systems, namely the discrete Smoluchowski and coagulation-fragmentation: we start by a brief description of the function spaces, and then review the results on existence of solutions with a brief description of the main ideas of the proofs. This part closes with the consideration of uniqueness results. In Sects. 3 and 4 we are concerned with several aspects of the solutions behaviour. We pay special attention to the long time convergence to equilibria, self-similar behaviour, and density conservation or lack thereof.

Keywords

Detailed Balance Condition Large Cluster Size Daughter Particle Coagulation Equation Strong Fragmentation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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Notes

Acknowledgements

I would like to thank Prof. Conceição Carvalho for the invitation to give an overview talk about the mathematics of coagulation equations at the thematic session on Non-Equilibrium Statistical Mechanics: Kinetics, Chemistry and Coagulation she organized as part of the International Conference on Mathematics of Energy and Climate Change, held in Lisbon, Portugal, in March 2013 and organized by CIM-Centro Internacional de Matemática.

I am also grateful to CIM president, Prof. Alberto Pinto, who enthusiastically supported my suggestion of writing this chapter by updating and translating into English an unpublished document I wrote in Portuguese a few years ago, and was very understanding in accepting the somewhat oversized result.

This work was partially supported by FCT under Strategic Project - LA 9 - 2013–2014.

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Authors and Affiliations

  1. 1.Departamento de Ciências e TecnologiaUniversidade AbertaLisboaPortugal
  2. 2.Centro de Análise Matemática, Geometria e Sistemas Dinâmicos, Departamento de Matemática, Instituto Superior TécnicoUniversidade de LisboaLisboaPortugal

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