Analytic Methods for Coagulation-Fragmentation Models Volume I

<p><strong><em>Analytic Methods for Coagulation-Fragmentation Models</em></strong> 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.</p><p>Features of Volume I:</p><ul> <p> </p> <li>The main models of the theory together with their derivations and early methods of solution</li> <p> </p> <li>A detailed presentation of the operator theoretical methods and semigroup theory that play an essential role in the theory of fragmentation processes</li> <p> </p> <li>A comprehensive theory of fragmentation processes including fragmentation with growth and decay in both the discrete and continuous particle size cases</li> <p> </p> <li>An analytical explanation of the `pathologies’ of the fragmentation equation such as the shattering phase transition and non-uniqueness of solutions</li> <p> </p> <li>An analysis of the long-term dynamics of the discrete size fragmentation equation with growth</li> </ul>