Steady-state solution for discrete Oort-Hulst-Safronov coagulation equation

Abstract

The paper examines the steady-state behaviour of the Safronov-Dubovski coagulation equation for the kernel Vi,j = CV (iβjγ + iγ jβ ) when 0 ≤ β ≤ γ ≤ 1, ( β + γ ) ∈ [0, 2] ∀ i, j ∈ ℕ, CV ∈ ℝ⁺. By assuming the boundedness of the second moment, the existence of a unique steady-state solution is established. Since, the model is non-linear and analytical solutions are not available for such cases, numerical simulations are performed to justify the theoretical findings. Four different test cases are considered by taking physically relevant kernels such as Vi,j = 2, (i + j), 8i1/2j1/2 and 2ij along with various initial conditions. The obtained results are reported in the form of graphs and tables.