Asymptotics behaviour in one dimensional model of interacting particles
Analysis of PDEs
2011-05-05 v1
Abstract
We consider the equation u_t=\epsilon u_{xx}+(u\ K'*u)_x for x\in\mathbb{R}, t>0 and with \epsilon\geq 0, supplemented with a nonnegative, integrable initial datum. We present a class of interaction kernels K' such that the large time behaviour of solutions to this initial value problem is described by a compactly supported self-similar profile.
Keywords
Cite
@article{arxiv.1105.0872,
title = {Asymptotics behaviour in one dimensional model of interacting particles},
author = {Rafał Celiński},
journal= {arXiv preprint arXiv:1105.0872},
year = {2011}
}