Analytic Methods for Coagulation-Fragmentation Models, Volume II

Jacek Banasiak, Wilson Lamb, Philippe Laurencot

• Publisher: CRC Press
• Year: 2019
• ISBN:
  9781000008159
• Edition: 1
• Topic: Mathematics
• Subtopic: Mathematical Analysis
• 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 II:

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• A primer on weak compactness in L 1 and dynamical systems

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• 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

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• A detailed analysis of the long-term dynamics of the coagulation-fragmentation equations with a state-of-the-art discussion on self-similar solutions

Table of contents

• Cover
• Half Title
• Title Page
• Copyright Page
• Dedication
• Table of Contents
• Preface
• About the Authors
• Symbol Description
• 6 Introduction to Volume II
• 7 Mathematical Toolbox II
• 8 Solvability of Coagulation-Fragmentation Equations
• 9 Gelation and Shattering
• 10 Long-Term Behaviour
• 11 Miscellanea
• Bibliography
• Index