Name
Title | ||
|---|---|---|
One-Dimensional Dissipative Boltzmann Equation: Measure Solutions, Cooling Rate, and Self-Similar Profile. |
Abstract | ||
|---|---|---|
This manuscript investigates the following aspects of the one-dimensional dissipative Boltzmann equation associated to a 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) we give existence and uniqueness of measure solutions, and (3) we prove the existence of a nontrivial 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. |
Year | DOI | Venue |
|---|---|---|
2018 | 10.1137/17M1136791 | SIAM JOURNAL ON MATHEMATICAL ANALYSIS |
Keywords | DocType | Volume |
Boltzmann equation,self-similar solution,measure solutions,dynamical fixed point | Journal | 50 |
Issue | ISSN | Citations |
1 | 0036-1410 | 0 |
PageRank | References | Authors |
0.34 | 0 | 4 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Ricardo J. Alonso | 1 | 2 | 2.26 |
| Véronique Bagland | 2 | 0 | 0.34 |
| Yingda Cheng | 3 | 201 | 20.27 |
| Bertrand Lods | 4 | 15 | 3.98 |