Advances in Differential Equations

Stationary solutions, intermediate asymptotics and large-time behaviour of type II Streater's models

Piotr Biler, Jean Dolbeault, Maria J. Esteban, and Grzegorz Karch

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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.

Article information

Source
Adv. Differential Equations, Volume 6, Number 4 (2001), 461-480.

Dates
First available in Project Euclid: 2 January 2013

Permanent link to this document
https://projecteuclid.org/euclid.ade/1357140608

Mathematical Reviews number (MathSciNet)
MR1798494

Zentralblatt MATH identifier
1003.35120

Subjects
Primary: 35Qxx: Equations of mathematical physics and other areas of application [See also 35J05, 35J10, 35K05, 35L05]
Secondary: 35B40: Asymptotic behavior of solutions 35J60: Nonlinear elliptic equations 35K55: Nonlinear parabolic equations 82C22: Interacting particle systems [See also 60K35]

Citation

Biler, Piotr; Karch, Grzegorz; Dolbeault, Jean; Esteban, Maria J. Stationary solutions, intermediate asymptotics and large-time behaviour of type II Streater's models. Adv. Differential Equations 6 (2001), no. 4, 461--480. https://projecteuclid.org/euclid.ade/1357140608


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