2023/06/15 by Barik, Prasanta Kumar, Dond, Asha K., Kumar, Rakesh
#Analysis of PDEs (math.AP) #FOS: Mathematics
paper · doi:10.48550/arxiv.2306.09168
This article is devoted to a generalized version of Smoluchowski's coagulation equation. This model describes the time evolution of a system of aggregating particles under the effect of external input and output particles. We show that for a large class of coagulation kernels, output rates, and exponentially decaying input rates, there is a weak solution. Moreover, the solution satisfies the mass-conservation property for linear coagulation rate and an additional condition on input and output rates. The uniqueness of weak solutions is also established by applying additional restrictions on the rates.