Analytic Methods for Coagulation-Fragmentation Models, Volume I

This comprehensive volume explores linear fragmentation models and foundational theories, making it a vital resource for understanding coagulation-fragmentation processes.

This two-volume set offers a thorough examination of coagulation-fragmentation models, starting with an extensive survey of the processes involved. The first volume, Analytic Methods for Coagulation-Fragmentation Models, Volume I, presents foundational concepts alongside early results related to the model equations. These insights provide a strong basis for understanding the more contemporary studies that have significantly advanced the theory, particularly regarding solvability and the long-term behavior of solutions.

Volume I focuses on linear fragmentation models, laying the groundwork for the mathematical analysis that follows. It introduces essential mathematical tools that are crucial for comprehending modern treatments, ensuring the text remains as self-contained as possible. The volume covers the main models of the theory, their derivations, and early solution methods, while also delving into operator theoretical methods and semigroup theory, which are vital to fragmentation processes.

In addition, readers will find a comprehensive theory of fragmentation processes, addressing both growth and decay in discrete and continuous particle sizes. The volume also tackles the complexities of the fragmentation equation, including phenomena such as the shattering phase transition and the non-uniqueness of solutions. An analysis of the long-term dynamics of the discrete size fragmentation equation with growth is also provided, making this an essential resource for researchers in the field.