Condensation phenomena in nonlinear drift equations

Abstract

We study non-negative, 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 / oo. Our analysis makes a substantial use of independent variable scalings and pseudo-inverse functions techniques.