Fragmentation--coagulation processes with advection or diffusion in space

In this paper, we consider a continuous fragmentation–coagulation model in which the reacting particles can be transported in physical space through either advection or diffusion. We prove new results on the generation of C 0 -semigroups with parameter and use them to show that the Abstract Cauchy Problem associated with a more general version of the advection/diffusion–fragmentation problem generates a positive C 0 -semigroup in spaces L 1 ( R + , X x , ( 1 + m r ) d m ) , where m is the particle mass, X x is either the space of integrable or continuous functions with respect to the spatial variable, and the weight exponent r is sufficiently large. These results enable us to prove the classical solvability of a wide range of advection/diffusion–fragmentation–coagulation equations with unbounded coagulation kernels.