Analytic Methods for Coagulation-Fragmentation Models, Volume I & II

1st Edition

Jacek Banasiak, Wilson Lamb, Philippe Laurencot

CRC Press
July 15, 2019 Forthcoming
Reference - 712 Pages - 3 B/W Illustrations
ISBN 9780367235444 - CAT# K422554
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 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:

  • Provides a comprehensive and up-to-date survey of knowledge and important results in the field, and brings together two different deterministic analytical approaches for solving the fundamental coagulation-fragmentation equations
  • Presents a state-of-the-art analysis of the long-term dynamics of the models
  • Offers an analytic explanation of phase transitions such as shattering and gelation, appearing for the first time in a book form
  • Includes a self-contained survey of essential mathematical tools from kinetic theory, with applications to specific, but nontrivial, examples of coagulation-fragmentation theory
  • Provides a link between phenomenological results obtained in applied and technological sciences and rigorous mathematical theory

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