Stationary solutions to Smoluchowski’s coagulation equation with source

Abstract

Existence and non-existence of integrable stationary solutions to Smoluchowski's coagulation equation with source are investigated when the source term is integrable with an arbitrary support in \((0,\infty)\). Besides algebraic upper and lower bounds, a monotonicity condition is required for the coagulation kernel. Connections between integrability properties of the source and the corresponding stationary solutions are also studied.