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 $\mathbb R^d$ space problems without exterior potential using time-dependent rescalings and show the existence of intermediate asymptotics in special cases.
Citation
Piotr Biler. Jean Dolbeault. Maria J. Esteban. Grzegorz Karch. "Stationary solutions, intermediate asymptotics and large-time behaviour of type II Streater's models." Adv. Differential Equations 6 (4) 461 - 480, 2001. https://doi.org/10.57262/ade/1357140608
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