@article{Brull2022, 
author = {Stéphane Brull and Marwa Shahine and Philippe Thieullen},
title = {Compactness property of the linearized Boltzmann operator for a diatomic single gas model},
year = {2022},
journal = {Networks and Heterogeneous Media},
volume = {17},
number = {6},
pages = {847-861},
keywords = {Diatomic gases, linearized Boltzmann operator, Fredholm alternative, continuous internal energy model},
url = {https://www.sciopen.com/article/10.3934/nhm.2022029},
doi = {10.3934/nhm.2022029},
abstract = {In the following work, we consider the Boltzmann equation that models a diatomic gas by representing the microscopic internal energy by a continuous variable I. Under some convenient assumptions on the collision cross-section        B  , we prove that the linearized Boltzmann operator        L   of this model is a Fredholm operator. For this, we write        L   as a perturbation of the collision frequency multiplication operator, and we prove that the perturbation operator        K   is compact. The result is established after inspecting the kernel form of        K   and proving it to be        L    2   integrable over its domain using elementary arguments.This implies that        K   is a Hilbert-Schmidt operator.}
}