Abstract :

We study a continuous coagulation-fragmentation model withconstant kernels for reacting polymers (the so-called Aizenmann-Bak model). 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.