Advances in Differential Equations

On a new model for continuous coalescence and breakage processes with diffusion

Christoph Walker

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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.

Article information

Source
Adv. Differential Equations Volume 10, Number 2 (2005), 121-152.

Dates
First available in Project Euclid: 18 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.ade/1355867886

Mathematical Reviews number (MathSciNet)
MR2106128

Zentralblatt MATH identifier
1107.47061

Subjects
Primary: 82C21: Dynamic continuum models (systems of particles, etc.)
Secondary: 35K57: Reaction-diffusion equations 45K05: Integro-partial differential equations [See also 34K30, 35R09, 35R10, 47G20] 76T99: None of the above, but in this section

Citation

Walker, Christoph. On a new model for continuous coalescence and breakage processes with diffusion. Adv. Differential Equations 10 (2005), no. 2, 121--152. https://projecteuclid.org/euclid.ade/1355867886.


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