Asymptotic behaviour of liquid-liquid dispersions

Based on earlier results on existence, we study the asymptotic behaviour of solutions to the coalescence-breakage equations, including the volume-scattering phenomenon and high-energy collisions. The solutions are shown to converge towards one particular equilibrium, provided the kernels satisfy a kind of reversibility. We also derive stability of these equilibria in a suitable topology. DOI: https://doi.org/10.1017/S0308210500003462 Posted at the Zurich Open Repository and Archive, University of Zurich ZORA URL: https://doi.org/10.5167/uzh-21827 Originally published at: Walker, Ch (2004). Asymptotic behaviour of liquid-liquid dispersions. Proceedings of the Royal Society of Edinburgh: Section A, 134(4):753-772. DOI: https://doi.org/10.1017/S0308210500003462 Proceedings of the Royal Society of Edinburgh, 134A, 753–772, 2004 Asymptotic behaviour of liquid–liquid dispersions Christoph Walker Institut für Mathematik, Universität Zürich-Irchel, Winterthurerstrasse 190, CH-8057 Zürich, Switzerland ([email protected]) (MS received 23 September 2003; accepted 18 February 2004) Based on earlier results on existence, we study the asymptotic behaviour of solutions to the coalescence-breakage equations, including the volume-scattering phenomenon and high-energy collisions. The solutions are shown to converge towards one particular equilibrium, provided the kernels satisfy a kind of reversibility. We also derive stability of these equilibria in a suitable topology.