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Trend to equilibrium solution for the discrete Safronov–Dubovskiĭ aggregation equation with forcing
Published online by Cambridge University Press: 16 November 2023
Abstract
We consider the discrete Safronov-Dubovskiĭ aggregation equation associated with the physical condition, where particle injection and extraction take place in the dynamical system. In application, this model is used to describe the aggregation of particle-monomers in combination with sedimentation of particle-clusters. More precisely, we prove well-posedness of the considered model for a large class of aggregation kernel with source and efflux coefficients. Furthermore, over a long time period, we prove that the dynamical model attains a unique equilibrium solution with an exponential rate under a suitable condition on the forcing coefficient.
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- Copyright © The Author(s), 2023. Published by Cambridge University Press on behalf of The Royal Society of Edinburgh