In this thesis, we examine an infinite system of ordinary differential equations that models the evolution of fragmenting and coalescing discrete-sized particle clusters.We express this discrete coagulationâfragmentation system as an abstract Cauchy problem posed in an appropriate Banach space of sequences. The theory of operator semigroups is then used to establish the existence and uniqueness of solutions. We also investigate properties of the solutions, such as positivity, mass conservation and asymptotic behaviour. A main aim of this thesis is to relax the assumptions that have previously been required, when using a semigroupapproach, to obtain the existence and uniqueness of physically relevant solutions.Moreover, we consider the case when the infinite system is non-autonomous dueto time-dependent coagulation and fragmentation coefficients.
|Date of Award||6 Feb 2020|
- University Of Strathclyde
|Supervisor||Matthias Langer (Supervisor) & Wilson Lamb (Supervisor)|