We consider existence, large-time behaviour and fast-reaction limits of coagulation-fragmentation models with spatial diffusion, which share many formal and structural  similarities with kinetic equations. As continuous-in-size model, we study Smoluchowski’s equation with constant coefficients and prove explicit convergence to equilibrium also in the case of degenerate diffusion coefficients.

Discrete-in-size models are considered with more general coefficients. The diffusion coefficients are also allowed to degenerate in size.

The main techniques include a-priori estimates based on the dissipation of an  entropy functional, entropy entropy-dissipation methods, moment bounds and  duality methods.