One dimensional dissipative Boltzmann equation: measure solutions, cooling rate and self-similar profile
Analysis of PDEs
2015-05-28 v1
Abstract
This manuscript investigates the following aspects of the one dimensional dissipative Boltzmann equation associated to variable hard-spheres kernel: (1) we show the optimal cooling rate of the model by a careful study of the system satisfied by the solution's moments, (2) give existence and uniqueness of measure solutions, and (3) prove the existence of a non-trivial self-similar profile, i.e. homogeneous cooling state, after appropriate scaling of the equation. The latter issue is based on compactness tools in the set of Borel measures. More specifically, we apply a dynamical fixed point theorem on a suitable stable set, for the model dynamics, of Borel measures.
Keywords
Cite
@article{arxiv.1505.07207,
title = {One dimensional dissipative Boltzmann equation: measure solutions, cooling rate and self-similar profile},
author = {Ricardo Alonso and Véronique Bagland and Yingda Cheng and Bertrand Lods},
journal= {arXiv preprint arXiv:1505.07207},
year = {2015}
}