APDEs Seminar

Abstract: Smoluchowski’s coagulation equation describes the evolution in time of a system of atmospheric particles, coagulating upon binary collision. In this talk, I will present a generalization of the classical Smoluchowski’s coagulation equation, i.e., the coagulation equation with a source term of small clusters. The source term drives the system out of equilibrium, leading to a rich range of different possible long-time behaviours, including anomalous self-similarity.
In this talk, we assume that the coagulation kernel is symmetric, non gelling, homogeneous, with homogeneity γ < 1, and behaves like x^(γ+λ) y^(−λ) when y << x, with γ+2λ ≥ 0. These kernels include some of the coagulation kernels relevant in atmospheric science.
We will discuss the existence of standard and anomalous self-similar solutions under different assumptions on the values of the parameters γ and λ.