Condensation phenomena in nonlinear drift equations

• José A. Carrillo ^[1] ; Marco Di Francesco ^[2] ; Giuseppe Toscani ^[3]
  1. [1] Imperial College London

     Imperial College London

     Reino Unido

     
  2. [2] University of Bath

     University of Bath

     Reino Unido

     
  3. [3] Università di Pavia, Italia

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• Localización: Annali della Scuola Normale Superiore di Pisa. Classe di scienze, ISSN 0391-173X, Vol. 15, Nº Extra 1 (Special volume), 2016, págs. 145-171
• Idioma: inglés
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• Resumen

  • We study non-negative, measure-valued solutions to nonlinear drifttype 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 → ∞. Our analysis makes a substantial use of independent variable scalings and pseudo-inverse functions techniques.