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.
- 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
Table of Contents
1 Basic Concepts
2 Coagulation and Fragmentation
3 Mathematical Toolbox I
4 Semigroup Methods for Fragmentation Models
5 Classical Solutions of Fragmentation Equations
6 Introduction to Volume II
7 Mathematical Toolbox II
8 Solvability of Coagulation-Fragmentation Equations
9 Gelation and Shattering
10 Long-Term Behaviour
Jacek Banasiak is a Professor of Mathematics at the University of Pretoria, South Africa, where he holds DST/NRF Research Chair in Mathematical Models and Methods in Biosciences and Bioengineering, and at Łódź University of Technology, Poland. His main research areas are functional analytic methods in kinetic theory and mathematical biology, singular perturbations, general applied analysis and partial differential equations and evolution problems. He is the author/co-author of 5 monographs and over 120 papers in these fields. He is also Editor-in-Chief of Afrika Matematika (Springer). In 2012 received the South African Mathematical Society Award for Research Distinction and in 2013 he was awarded the Cross of Merit (Silver) of the Republic of Poland.
Wilson Lamb is a Senior Lecturer at the University of Strathclyde, Scotland. His main interests lie in Functional Analysis, Applied Analysis, Evolution Equations, Mathematical Analysis of Coagulation and Fragmentation Processes. He has published over 45 refereed research publications. He has given lecture courses at all levels to Mathematics degree students and to Science and Engineering students. These include courses on elementary calculus and algebra, discrete mathematics, multivariable calculus, linear algebra and vector space theory. He was nominated for the University of Strathclyde Students’ Association Teaching Excellence Awards in 2012, 2013 and 2014; in 2013, he was shortlisted for the category of “Best in Science Faculty”.
Philippe Laurençot is the Director of research (senior researcher) CNRS 1, Institut de Math ematiques de Toulouse, Universite Paul Sabatier. His main research interests include the mathematical analysis of evolution partial differential equations,dynamical system approach to evolution partial differential equations, coagulation equations and mathematical models in biology. He is the author of over 170 scientific publications and has given invited talks all over the world.