Large Time Asymptotics for a Continuous Coagulation-Fragmentation Model with Degenerate Size-Dependent Diffusion

We study a continuous coagulation-fragmentation model with constant kernels for reacting polymers (see [AB]). The polymers are set to diffuse within a smooth bounded domain with no-flux boundaries. In particular, we consider size-dependent diffusion coefficients, which may degenerate for small and large cluster-sizes. We prove that the entropy-entropy dissipation method applies directly in this inhomogeneous setting. We first show the necessary basic a priori estimates in dimension one, and secondly, we show faster-than-polynomial convergence towards global equilibria for diffusion coefficients, which vanish not faster than linearly for large sizes.