EXISTENCE AND UNIQUENESS FOR SPATIALLY INHOMOGENEOUS COAGULATION EQUATION WITH SOURCES AND EFFLUXES

We prove the local existence theorem for general Smoluchovsky's coagul ation equation with coagulation kernels which allow the multiplicative growth. If the system concerned has absorption, then the local existe nce theorem converts into the global existence theorem provided that i nitial data and sources are sufficiently small. We prove uniqueness, m ass conservation and continuous dependence on initial data in the doma in of its existence. We show that the solution ''in large'' asymptotic ally tends to zero as time goes to infinity and demonstrate that, in g eneral, the sequence of approximated solutions does not converge to th e exact solution of the original problem with the multiplicative kerne l. This fact reveals the limits of numerical simulation of the coagula tion equation.