Condensation phenomena in nonlinear drift equations
Analysis of PDEs
2013-07-10 v1
Abstract
We study nonnegative, measure-valued solutions to nonlinear drift type equations modelling concentration phenomena related to Bose-Einstein particles. In one spatial dimension, we prove existence and uniqueness for measure solutions. Moreover, we prove that all solutions blow up in finite time leading to a concentration of mass only at the origin, and the concentrated mass absorbs increasingly the mass converging to the total mass as time goes to infinity. Our analysis makes a substantial use of independent variable scalings and pseudo-inverse functions techniques.
Cite
@article{arxiv.1307.2275,
title = {Condensation phenomena in nonlinear drift equations},
author = {Jose' A. Carrillo and Marco Di Francesco and Giuseppe Toscani},
journal= {arXiv preprint arXiv:1307.2275},
year = {2013}
}