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

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 e(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 e. The long‐term behavior of e is also discussed.