Analytic Methods for Coagulation-Fragmentation Models, Volume II

1st Edition

Jacek Banasiak, Wilson Lamb, Philippe Laurencot

CRC Press
July 15, 2019 Forthcoming
Reference - 336 Pages
ISBN 9780367235482 - CAT# K422558
Series: Chapman & Hall/CRC Monographs and Research Notes in Mathematics

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Summary

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 II:

  • A primer on weak compactness in L 1 and dynamical systems
  • A comprehensive theory of solvability of the coagulation-fragmentation equation by both the semigroup and weak compactness methods, including a thorough analysis of the gelation and shattering phenomena
  • A detailed analysis of the long-term dynamics of the coagulation-fragmentation equations with a state-of-the-art discussion on self-similar solutions