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Trend to equilibrium solution for the discrete Safronov–Dubovskiĭ aggregation equation with forcing

Part of: General theory in ordinary differential equations Equations of mathematical physics and other areas of application Applications - Dynamical systems and ergodic theory Equations and inequalities involving nonlinear operators

Published online by Cambridge University Press:  16 November 2023

Arijit Das Open the ORCID record for Arijit Das [Opens in a new window]  and
Jitraj Saha Open the ORCID record for Jitraj Saha [Opens in a new window]
Arijit Das
Affiliation:
Department of Mathematics, National Institute of Technology Tiruchirappalli, Tamil Nadu 620015, India (arijitdasnitt@gmail.com;jitraj@nitt.edu)
Jitraj Saha
Affiliation:
Department of Mathematics, National Institute of Technology Tiruchirappalli, Tamil Nadu 620015, India (arijitdasnitt@gmail.com;jitraj@nitt.edu)
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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.

Keywords

Safronov–Dubovskiĭ aggregation equationforcing coefficientswell-posednessequilibrium solutionexponential convergence

MSC classification

Primary: 34A12: Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions 35Q70: PDEs in connection with mechanics of particles and systems 37N05: Dynamical systems in classical and celestial mechanics
Secondary: 47J35: Nonlinear evolution equations
Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , First View , pp. 1 - 24
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Copyright
Copyright © The Author(s), 2023. Published by Cambridge University Press on behalf of The Royal Society of Edinburgh

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