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arXiv · 1603.02929

Oscillatory dynamics in Smoluchowski's coagulation equation with diagonal kernel

Philippe Laurençot·Barbara Niethammer·Juan J. L. Velázquez
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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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Philippe Laurençot, Barbara Niethammer, Juan J. L. Velázquez. 2016-08-10. Oscillatory dynamics in Smoluchowski's coagulation equation with diagonal kernel. https://arxiv.org/abs/1603.02929

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