Oscillatory dynamics in Smoluchowski's coagulation equation with diagonal kernel

2016/03/09 by Philippe Laurençot, Barbara Niethammer, Laurençot, Philippe +3
Medicine · Computer Science · Mathematics · #Mathematical and Theoretical Epidemiology and Ecology Models #Advanced Mathematical Modeling in Engineering #Differential Equations and Numerical Methods

paper · pdf · doi:10.48550/arxiv.1603.02929

Abstract

We characterize the long-time behaviour of solutions to Smoluchowski's coagulation equation with a diagonal kernel of homogeneity γ< 1. Due to the property of the diagonal kernel, the value of a solution depends only on a discrete set of points. As a consequence, the long-time behaviour of solutions is in general periodic, oscillating between different rescaled versions of a self-similar solution. Immediate consequences of our result are a characterization of the set of data for which the solution converges to self-similar form and a uniqueness result for self-similar profiles.

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