Calculus of Variations and Geometric Measure Theory
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J. A. Carrillo - M. Di Francesco - G. Toscani

Condensation phenomena in nonlinear drift equations

created by difrancesco on 08 Jul 2013

[BibTeX]

Preprint

Inserted: 8 jul 2013

Year: 2013
Links: PDF

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 $t\to\infty$. Our analysis makes a substantial use of independent variable scalings and pseudo-inverse functions techniques.

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