The effect of particle coagulation on the diffusive relaxation of a spatially inhomogeneous aerosol

Global existence for the discrete diffusive coagulation-fragmentation equations in $L^1$

“…and the right-hand side of the above inequality is bounded uniformly with respect to N by (19), (23). Consequently, the claim (24) holds true for each j ∈ {1, .…”

“…Fix i ≥ 1. It follows from (19), (23) and (24) that, for each N ≥ 1, c N i is a solution to a linear heat equation with initial data and right-hand sides uniformly bounded in L 1 (Ω) and L 1 (Ω T ), respectively. Since A 1 generates a positive, compact and analytic semigroup in L 1 (Ω) by [1] we are thus in a position to apply the compactness results of [5,4] and conclude that (c N i ) N is relatively strongly compact in L 1 (Ω T ).…”

“…Owing to (19), (27) and (32) it is straightforward to pass to the limit in the mild formulation (15) of (1) and conclude that c is a weak solution to (1)-(3) (observe that we may take T to be an arbitrary large integer and perform countably many successive extractions).…”

“…Let us mention here that the original model proposed by Smoluchowski was introduced to analyze the binary coagulation of colloids moving according to brownian motions and several additional physical processes have been subsequently incorporated into the model (fragmentation, condensation, influence of external fields, see, e.g., [10]). The field of applications of the Smoluchowski model has meanwhile widened and now includes, among others, aerosol science (evolution of a system of solid or liquid particles suspended in a gas [10,19]), astrophysics (formation of the planets [18]), polymer science and hematology (red blood cell aggregation [17]). We refer to [10] for derivations of the model, together with some physical background.…”

Coagulation in a diffusing Gaussian aerosol puff: Comparison of analytical approximations with numerical solutions

“…Simons (1987Simons ( , 1992Simons ( , 1996 conducted a series of studies on the solution of one-dimensional steady state coagulation-diffusion equation considering both constant and size dependent diffusion coefficient and coagulation kernels. Simons and Simpson (1988) combined scaling theory with moment method to reduce the diffusion-coagulation equation in three dimensions to simpler nonlinear form of recombination-diffusion equation, which, however, cannot be solved analytically.…”