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\begin{document}

\title{Asymptotic analysis of time dependent solutions for the coagulation
equation with source and efflux}



\author[1]{Debdulal Ghosh}%
\author[2]{Lukas  Pflug}%
\author[1]{Jitendra  Kumar}%
\affil[1]{Indian Institute of Technology Kharagpur}%
\affil[2]{Friedrich-Alexander-Universität Erlangen-Nürnberg}%


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  \date{May 27, 2024}


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\begin{abstract}
This article provides mathematical proof of the existence of stationary
solutions for the coagulation equation including source and efflux
terms. We demonstrate the convergence of time dependent solutions to
these stationary solutions and highlight the exponential rate of
convergence. These properties are analyzed for affine linear coagulation
kernels, non-negative source terms and positive efflux rates. Numerical
examples are included to demonstrate the predicted convergence
behaviour.%
\end{abstract}%



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