Résumé en anglais

The authors consider type II Streater's models which describe the coupled evolution of the density of a cloud of particles in an external potential with non-constant temperature. Energy is preserved. The authors introduce an entropy and investigate stationary solutions in a bounded domain, or in an unbounded domain with confining external potential. Existence and uniqueness results for stationary solutions are established. The entropy is re-interpreted as a relative entropy which controls the convergence to stationary solutions. Also, the whole-space setting without exterior potential is considered. The authors employ time-dependent scalings and show existence of intermediate asymptotics in special cases.