DOI: 10.24193/fpt-ro.2024.2.08

Authors: D. Ghosh, J. Paul, J. Kumar and J.-C. Yao

Abstract: The study of the coagulation-fragmentation model has provided insights into various engineering and scientific disciplines. However, the characteristics of particle ensembles are determined by multiple parameters in a multidimensional parameter space, including mass, volume, porosity, binder content, enthalpy, mole number, and more. This work focuses on establishing the existence of a continuous solution for the higher dimensional model, subject to certain restrictions on the kernels. Additionally, the conservation of volume of the solution are investigated. The results are derived based on the compactness result of Arzelà-Ascoli and the Banach contraction mapping principle.

Key Words and Phrases: Population balance model, coagulation, fragmentation, multi-dimension, contraction, fixed point, existence, volume conservation.

2010 Mathematics Subject Classification: 45J05, 34A34, 45L10, 47H10.

Published on-line: June 15th, 2024.

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