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

Authors: Sonali Kaushik; Rajesh Kumar

Addresses: Department of Mathematics, BITS Pilani, Pilani Campus, Rajasthan, 333031, India ' Department of Mathematics, BITS Pilani, Pilani Campus, Rajasthan, 333031, India

Abstract: The paper examines the steady-state behaviour of the Safronov-Dubovski coagulation equation for the kernel V_i,j = C_V (i^β j^γ + i^γ j^β ) when 0 ≤ β ≤ γ ≤ 1, ( β + γ ) ∈ [0, 2] ∀ i, j ∈ ℕ, C_V ∈ 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 V_i,j = 2, (i + j), 8_i^1/2_j^1/2 and 2_ij along with various initial conditions. The obtained results are reported in the form of graphs and tables.

Keywords: Safronov-Dubovski coagulation; existence; uniqueness; steady-state solution; moments.

DOI: 10.1504/IJDSDE.2023.130311

International Journal of Dynamical Systems and Differential Equations, 2023 Vol.13 No.2, pp.144 - 163

Accepted: 14 Jul 2022
Published online: 17 Apr 2023 *

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