  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.
