Existence and uniqueness of weak solutions to the Smoluchowski coagulation equation with source and sedimentation

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...

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Bibliographic Details
Main Authors Barik, Prasanta Kumar, Dond, Asha K, Kumar, Rakesh
Format Journal Article
LanguageEnglish
Published 15.06.2023
Subjects
Mathematics - Analysis of PDEs
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Summary: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.
DOI:10.48550/arxiv.2306.09168