ON A MODEL FOR MASS AGGREGATION WITH MAXIMAL SIZE

Journal article

We study a kinetic mean-field equation for a system of particles with different sizes, in which particles are allowed to coagulate only if their sizes sum up to a prescribed time-dependent value. We prove well-posedness of this model, study the existence of self-similar solutions, and analyze the largetime behavior mostly by numerical simulations. Depending on the parameter k 0, which controls the probability of coagulation, we observe two different scenarios: For k 0 > 2 there exist two self-similar solutions to the mean field equation, of which one is unstable. In numerical simulations we observe that for all initial data the rescaled solutions converge to the stable self-similar solution. For k 0 < 2, however, no self-similar behavior occurs as the solutions converge in the original variables to a limit that depends strongly on the initial data. We prove rigorously a corresponding statement for k 0 ∈ (0, 1/3). Simulations for the cross-over case k 0 = 2 are not completely conclusive, but indicate that, depending on the initial data, part of the mass evolves in a self-similar fashion whereas another part of the mass remains in the small particles. © American Institute of Mathematical Sciences.

Authors: Budac, O; Herrmann, M; Niethammer, B; Spielmann, A

• Publication status: Published
• Journal: KINETIC AND RELATED MODELS
• Volume: 4
• Issue: 2
• Pages: 427-439
• Publication date: 2011-06-01
• DOI: 10.3934/krm.2011.4.427
• EISSN: 1937-5077
• ISSN: 1937-5093
• Language: English
• Keywords: coarsening in coagulation models; Aggregation with maximal size; self-similar solutions