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 + x
λ + y
λ
(xy)
σ
,
where 0 ≤ σ ≤
1
2
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.
