Executive Summary : | Particulate processes involve the interaction of particles moving in random motion, resulting in changes in shape, size, and mass. The Smoluchowki model, first proposed in 1916, describes the time evolution of particle size distribution due to aggregation in a closed dynamical system. In 1972, Oort-Hulst-Safronov (OHS) proposed a new mathematical model, where two colliding cosmic particles aggregate, leading to the formation of large astronomical bodies like asteroids, meteors, and planets. However, the OHS aggregation model is less explored due to its complex and nonlinear formulation and lack of high-speed computing. This project aims to address the detailed mathematical and numerical treatment of integro-partial differential equations describing OHS aggregation equations. The study proposes analyzing both the mathematical and numerical aspects of the OHS model, incorporating physical properties like source and sink terms during particle formation. The study also emphasizes the importance of large-time analysis for studying steady-state behavior in PBEs. The project also proposes solving the model numerically using efficient numerical models, as exact solutions may not be available for the system. |