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Stability for a class of equilibrium solutions to the coagulation-fragmentation equation

Lamb, W. and Stewart, I.W. (2008) Stability for a class of equilibrium solutions to the coagulation-fragmentation equation. In: Numerical Analysis and Applied Mathematics: International Conference on Numerical Analysis and Applied Mathematics. AIP Conference Proceedings, 1048 . American Institute of Physics, pp. 942-945. ISBN 978-0-7354-0576-9

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We consider the behaviour of solutions to the continuous constant-rate coagulation-fragmentation equation in the vicinity of an equilibrium solution. Semigroup methods are used to show that the governing linear equation for a perturbation epsilon(x,t) has a unique globally defined solution for suitable initial conditions. In addition, Laplace transforms and the method of characteristics lead to an explicit formula for epsilon. The long-term behavior of epsilon is also discussed.