Global classical solutions of coagulation-fragmentation equations with unbounded coagulation rates

We study discrete fragmentation coagulation equations in spaces X_p, p>1, consisting of distributions having the pth moments finite. We show that for sufficiently regular fragmentation laws the fragmentation semigroup is analytic in X_p, and fully characterize the domain of its generator. This allows for explicit characterization of the domains of the fractional powers of the generator through real interpolation. Finally, we use the linear results to show the existence of global classical solutions to fragmentation coagulation equations for a class of unbounded coagulation kernels.