Oscillatory dynamics in Smoluchowski's coagulation equation with diagonal kernel
Analysis of PDEs
2016-08-11 v2
Abstract
We characterize the long-time behaviour of solutions to Smoluchowski's coagulation equation with a diagonal kernel of homogeneity . 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.
Cite
@article{arxiv.1603.02929,
title = {Oscillatory dynamics in Smoluchowski's coagulation equation with diagonal kernel},
author = {Philippe Laurençot and Barbara Niethammer and Juan J. L. Velázquez},
journal= {arXiv preprint arXiv:1603.02929},
year = {2016}
}