Analytic Methods for Coagulation-Fragmentation Models, Volume I

Jacek Banasiak, Wilson Lamb, Philippe Laurencot

• Publisher: Chapman and Hall/CRC
• Year: 2019
• ISBN:
  9781351650465
• Edition: 1
• Topic: Mathematics
• Subtopic: Differential Equations
• Index: Mathematics

Analytic Methods for Coagulation-Fragmentation Models is a two-volume set that provides a comprehensive exposition of the mathematical analysis of coagulation-fragmentation models. Initially, an in-depth survey of coagulation-fragmentation processes is presented, together with an account of relevant early results obtained on the associated model equations. These provide motivation for the subsequent detailed treatment of more up-to-date investigations which have led to significant theoretical developments on topics such as solvability and the long-term behaviour of solutions. To make the account as self-contained as possible, the mathematical tools that feature prominently in these modern treatments are introduced at appropriate places. The main theme of Volume I is the analysis of linear fragmentation models, with Volume II devoted to processes that involve the nonlinear contribution of coagulation.

Features of Volume I:

• The main models of the theory together with their derivations and early methods of solution

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• A detailed presentation of the operator theoretical methods and semigroup theory that play an essential role in the theory of fragmentation processes

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• A comprehensive theory of fragmentation processes, including fragmentation with growth and decay in both the discrete and continuous particle size cases

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• An analytical explanation of the `pathologies' of the fragmentation equation, such as the shattering phase transition and non-uniqueness of solutions

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• An analysis of the long-term dynamics of the discrete size fragmentation equation with growth

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