dc.contributor.author |
Bisi, M. |
dc.contributor.author |
Carrillo de la Plata, José Antonio |
dc.contributor.author |
Toscani, Giuseppe |
dc.contributor.author |
Universitat Autònoma de Barcelona. Centre de Recerca Matemàtica |
dc.date |
2005 |
dc.identifier |
https://ddd.uab.cat/record/44164 |
dc.identifier |
urn:oai:ddd.uab.cat:44164 |
dc.identifier |
urn:10.1007/s10955-004-8785-5 |
dc.identifier |
urn:oai:egreta.uab.cat:publications/0c4d0a0f-2605-4746-a554-52cdb29d9b95 |
dc.identifier |
urn:scopus_id:33748908493 |
dc.format |
application/pdf |
dc.language |
eng |
dc.publisher |
Centre de Recerca Matemàtica |
dc.relation |
Centre de Recerca Matemàtica. Prepublicacions ; |
dc.rights |
open access |
dc.rights |
Aquest document està subjecte a una llicència d'ús de Creative Commons, amb la qual es permet copiar, distribuir i comunicar públicament l'obra sempre que se'n citin l'autor original, la universitat i el centre i no se'n faci cap ús comercial ni obra derivada, tal com queda estipulat en la llicència d'ús |
dc.rights |
https://creativecommons.org/licenses/by-nc-nd/2.5/ |
dc.subject |
Transport, Teoria del |
dc.subject |
Sobolev, Espais de |
dc.title |
Contractive metrics for a Boltzmann equation for granular gases: diffusive equilibriaThe Patterson-Sullivan embedding and minimal volume entropy for outer space |
dc.type |
Article |
dc.type |
Prepublicació |
dc.description.abstract |
We quantify the long-time behavior of a system of (partially) inelastic particles in a stochastic thermostat by means of the contractivity of a suitable metric in the set of probability measures. Existence, uniqueness, boundedness of moments and regularity of a steady state are derived from this basic property. The solutions of the kinetic model are proved to converge exponentially as t→ ∞ to this diffusive equilibrium in this distance metrizing the weak convergence of measures. Then, we prove a uniform bound in time on Sobolev norms of the solution, provided the initial data has a finite norm in the corresponding Sobolev space. These results are then combined, using interpolation inequalities, to obtain exponential convergence to the diffusive equilibrium in the strong L¹-norm, as well as various Sobolev norms. |