Open AccessStationary Boltzmann equation: an approach via Morse theory
Author(s) -
Rafael Galeano Andrades,
Joel Torres del Valle
Publication year - 2021
Publication title -
proyecciones
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.226
H-Index - 12
eISSN - 0717-6279
pISSN - 0716-0917
DOI - 10.22199/issn.0717-6279-4034
Subject(s) - morse code , boltzmann equation , mathematics , boltzmann constant , morse potential , boltzmann machine , statistical physics , mathematical physics , mathematical analysis , physics , thermodynamics , computer science , quantum mechanics , artificial neural network , telecommunications , machine learning
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.