Convergence of the discrete Redner-Ben-Avraham-Kahng coagulation equation

Abstract

This article looks at the relationship between the discrete and the continuous Redner-Ben-Avraham-Kahng (RBK) coagulation models. On the basis of a priori estimation, a weak stability principle and the weak compactness in $L_1$ for the continuous RBK model is shown. By employing a sequence of discrete models to approximate the continuous one, we show that how discrete model eventually converges to the the modified continuous one using the stability principle.