Preliminary group classification and exact solutions of Smoluchowski equation with a source

Abstract

Population balance equations are essential to scientists and engineers of widely varying discipline, applications have covered a wide range of processes involving bioreactors, catalytic reaction, and cell populations, but the lack of exact solutions necessitates the use of numerical methods. Group classification of Smoluchowski equation with a source is provided by use of the method of preliminary group classification. The determining equation is successfully solved by the method of developed Lie group analysis. All source functions, reduced equations, invariant solutions, explicit exact solutions and dynamic behavior analysis of solutions are presented in this paper.