Advances in Differential Equations

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

Christoph Walker

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text


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

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.

Export citation