Large time asymptotics for Fermi–Dirac statistics coupled to a Poisson equation

• Lanoir Addala ^[1]
  1. [1] ISSAT Sousse: Institut Superieur des Sciences Appliquees et de Technologie de Sousse
• Localización: SeMA Journal: Boletín de la Sociedad Española de Matemática Aplicada, ISSN-e 2254-3902, ISSN 2254-3902, Vol. 80, Nº. 3, 2023, págs. 381-391
• Idioma: inglés
• DOI: 10.1007/s40324-022-00303-3
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• Resumen

  • This paper deals with the large time behaviour of the solutions of nonlinear Vlasov–Poisson–Fokker–Planck system in presence of an external potential of confinement. The statistics of collisions we are considering here, is the Fermi–Dirac operator with the Pauli exclusion term and without the detailed balance principle. A hypocoercivity method and a notion of scalar product adapted to the presence of a Poisson coupling are used to prove the exponential convergence of the solution of our system.