Stationary Boltzmann equation: an approach via Morse theory
Author
Galeano, Rafael
Torres del Valle, Joel
Full text
https://www.revistaproyecciones.cl/index.php/proyecciones/article/view/403410.22199/issn.0717-6279-4034
Abstract
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.