Brownian coagulation

Abstract

Abstract. We consider a stochastic particle model for coagulating particles, whose free motion is Brownian, with diffusivity given by Einstein's law. We present in outline a derivation from this model of a spatially inhomogeneous version of Smoluchowski's coagulation equation. Some analytic results on existence, uniqueness and mass conservation for the limit equation are also presented.

Phytoplankton Dynamics: from the Behavior of Cells to a Transport Equation

“…In our models we also obtain a limit but here this limit is deterministic. Similar approach was applied to a model of coagulation with diffusion by Norris [35]. Measure-valued limits of interacting particle systems leading to the so-called generalized Smoluchowski equations were also considered in [8,16,24,27,43].…”

Spatial coagulation with bounded coagulation rate

“…This heuristic result was proved in an important special case by Norris in [12] and later in [4] and [14] by Hammond, Rezakhanlou, and Yaghouti. Well-posedness for equation (1.1) has been investigated in a relatively small number of works.…”

An asymptotically stable scheme for diffusive coagulation-fragmentation models

“…Indeed, convergence as R → ∞ is still true, but it is unclear whether one obtains conservation of the total volume in the limit R → ∞ (for kernels for which it is expected to hold, of course). We refer for instance to [22,31,34] for global weak solutions and [2] for local smooth solutions. Thus, in this paper we will focus only on the convergence of a sequence built on a numerical scheme towards a solution to Equation (2.7) when the truncature R is fixed.…”