SMOLUCHOWSKI COAGULATION EQUATION WITH VELOCITY DEPENDENCE.

We introduce a variant of the Smoluchowski coagulation equation as a kinetic equation with both position and velocity variables, which arises as the scaling limit of a system of second-order microscopic coagulating particles. We focus on the rigorous study of the PDE system in the spatially homogeneous case, proving existence and uniqueness under different initial conditions in suitable weighted spaces, investigating also the regularity of such solutions. [ABSTRACT FROM AUTHOR]