Fragmentation–Coagulation Processes With Advection or Diffusion in Space

ABSTRACT 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 ‐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 ‐semigroup in spaces where is the particle mass, is the space of either integrable or continuous functions with respect to the spatial variable, and the weight exponent 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.