On equilibrium solution to a singular coagulation equation with source and efflux

Abstract

In this study, we analyze the existence of a steady-state solution to a coagulation equation with source and efflux for the following singular coagulation kernel: K(x,y)=1+xλ+yλ(xy)σ,where 0≤σ≤12 and 0≤λ−σ≤1. The uniqueness of the steady-state solution is found in the space of functions which are continuous in (0,∞). Also, we find an explicit form of the equilibrium solution to the problem with sources and effluxes for the constant and product kernels; further, for a linear kernel, we provide a closed-form of the equilibrium solution. We provide a numerical example to support the proposed study.