Analysis and simulations of the discrete fragmentation equation with decay. (17th November 2017)

• Record Type: Journal Article
• Authors: Banasiak, J.; Joel, L. O.; Shindin, S.
• Is Part Of: Mathematical methods in the applied sciences. Volume 41:Number 16(2018)
• Page Start: 6530
• Page End: 6545
• Publication Date: 2017-11-17
• Subjects: asynchronous exponential growth -- C0 semigroups -- discrete fragmentation -- death process -- long‐term behaviour -- numerical simulations -- spectral gap; Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.4666
• Languages: English
• ISSNs: 0170-4214

Abstract

Abstract : Fragmentation‐coagulation processes, in which aggregates can break up or get together, often occur together with decay processes in which the components can be removed from the aggregates by a chemical reaction, evaporation, dissolution, or death. In this paper, we consider the discrete decay‐fragmentation equation and prove the existence and uniqueness of physically meaningful solutions to this equation using the theory of semigroups of operators. In particular, we find conditions under which the solution semigroup is analytic, compact, and has the asynchronous exponential growth property. The theoretical analysis is illustrated by a number of numerical simulations.