Stationary Boltzmann equation: an approach via Morse theory

• Galeano, Rafael ^[1] ; Torres del Valle, Joel ^[2]
  1. [1] Universidad de Cartagena

     Universidad de Cartagena

     Colombia

     
  2. [2] Universidad de Antioquia

     Universidad de Antioquia

     Colombia

     
• Localización: Proyecciones: Journal of Mathematics, ISSN 0716-0917, ISSN-e 0717-6279, Vol. 40, Nº. 6, 2021, págs. 1473-1487
• Idioma: inglés
• DOI: 10.22199/issn.0717-6279-4034
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• Resumen

  • In this paper we study the unidimensional Stationary Boltzmann Equation by an approach via Morse theory. We define a functional J whose critical points coincide with the solutions of the Stationary Boltzmann Equation. By the calculation of Morse index of J’’0(0)h and the critical groups C2(J, 0) and C2(J, ∞) we prove that J has two different critical points u1 and u2 different from 0, that is, solutions of Boltzmann Equation.

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