Cahiers du CEREMADE

Unité Mixte de Recherche du C.N.R.S. N°7534
 
Abstract : In this paper, we study type II Streater's models. These models describe the coupled evolution of the density of a cloud of particles in an external potential and a temperature, preserving the energy, with eventually a nonlocal Poisson coupling. We introduce an entropy and consider in a bounded domain, or in an unbounded domain with a~confining external potential, the stationary solutions (with given mass and energy), for which we have existence and uniqueness results. The entropy is reinterpreted as a relative entropy which controls the convergence to the stationary solutions. We consider also the whole $R^d$ space problems without exterior potential using time-dependent rescalings and show the existence of intermediate asymptotics in special cases.
 
 
STATIONARY SOLUTIONS, INTERMEDIATE ASYMPTOTIC AND LARGE TIME BEHARVIOUR OF TYPE II STREATER'S MODELS
BILER Piotr, DOLBEAULT Jean, ESTEBAN Maria J.
2000-24
19-06-2000
 
Université de PARIS - DAUPHINE
Place du Maréchal de Lattre De Tassigny - 75775 PARIS CEDEX 16 - FRANCE
Téléphone : +33 (0)1 44-05-49-23 - fax : +33 (0)1 44-05-45-99