Existence and uniqueness for spatially inhomogeneous coagulation equation with sources and effluxes

Abstract

We prove the local existence theorem for general Smoluchovsky's coagulation equation with coagulation kernels which allow the multiplicative growth. If the system concerned has absorption, then the local existence theorem converts into the global existence theorem provided that initial data and sources are sufficiently small. We prove uniqueness, mass conservation and continuous dependence on initial data in the domain of its existence. We show that the solution “in large” asymptotically tends to zero as time goes to infinity and demonstrate that, in general, the sequence of approximated solutions does not converge to the exact solution of the original problem with the multiplicative kernel. This fact reveals the limits of numerical simulation of the coagulation equation.