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2005 On a new model for continuous coalescence and breakage processes with diffusion
Christoph Walker
Adv. Differential Equations 10(2): 121-152 (2005).

Abstract

We study a new model for the evolution of a liquid-liquid dispersion. The droplets of the dispersed phase are supposed to move due to diffusion and to undergo coalescence and breakage. The main feature of the model is the inclusion of a maximal droplet size. This requires a consistent mechanism opposing the increase of droplets due to coalescence. The resulting system of uncountably many coupled reaction-diffusion equations is interpreted as a vector-valued Cauchy problem. We prove existence and uniqueness of nonnegative and mass-preserving solutions. Furthermore, we give sufficient conditions for global existence.

Citation

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Christoph Walker. "On a new model for continuous coalescence and breakage processes with diffusion." Adv. Differential Equations 10 (2) 121 - 152, 2005.

Information

Published: 2005
First available in Project Euclid: 18 December 2012

zbMATH: 1107.47061
MathSciNet: MR2106128

Subjects:
Primary: 82C21
Secondary: 35K57, 45K05, 76T99

Rights: Copyright © 2005 Khayyam Publishing, Inc.

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