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Title:
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Contractive metrics for a Boltzmann equation for granular gases: diffusive equilibriaThe Patterson-Sullivan embedding and minimal volume entropy for outer space
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Author:
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Bisi, M.; Carrillo, José A.; Toscani, Giuseppe
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Other authors:
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Centre de Recerca Matemàtica |
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Abstract:
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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. |
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Publication date:
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2005-03 |
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Subject(s):
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Transport, Teoria del
Sobolev, Espais de |
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Rights:
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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 (http://creativecommons.org/licenses/by-nc-nd/2.5/es/) |
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Document type:
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Preprint |
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