Advances in Differential Equations
- Adv. Differential Equations
- Volume 10, Number 2 (2005), 121-152.
On a new model for continuous coalescence and breakage processes with diffusion
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.
Adv. Differential Equations Volume 10, Number 2 (2005), 121-152.
First available in Project Euclid: 18 December 2012
Permanent link to this document
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
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
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