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arXiv · 1307.2275

Condensation phenomena in nonlinear drift equations

Jose' A. Carrillo·Marco Di Francesco·Giuseppe Toscani
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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.

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Jose' A. Carrillo, Marco Di Francesco, Giuseppe Toscani. 2013-07-08. Condensation phenomena in nonlinear drift equations. https://arxiv.org/abs/1307.2275

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