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Author Budáč, Ondrej ♦ Herrmann, Michael ♦ Niethammer, Barbara ♦ Spielmann, Andrej
Source CiteSeerX
Content type Text
File Format PDF
Subject Domain (in DDC) Computer science, information & general works ♦ Data processing & computer science
Abstract 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 timedependent value. We prove well-posedness of this model, study the existence of self-similar solutions, and analyze the large-time behavior mostly by numerical simulations. Depending on the parameter k0, which controls the strength of coagulation probability, we observe two different scenarios: For k0> 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, so when time proceeds the total mass is shifted to larger and larger particles. For k0 < 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 can rigorously prove a corresponding statement for k0 ∈ (0,1/3). Simulations for the cross-over case k0 = 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. Keywords: MSC (2000): aggregation with maximal size, self-similar solutions, coarsening in coagulation models 45K05, 82C22 1
Educational Role Student ♦ Teacher
Age Range above 22 year
Educational Use Research
Education Level UG and PG ♦ Career/Technical Study