On the one-dimensional version of the dynamical Marguerre-Vlasov system with thermal effects

Gustavo Alberto Perla Menzala; Julian Moises Sejje Suárez

doi:10.3934/proc.2009.2009.536

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2009, Volume 2009: 536-547. Doi: 10.3934/proc.2009.2009.536 open access

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On the one-dimensional version of the dynamical Marguerre-Vlasov system with thermal effects

1.
National Laboratory of Scientific Computation, LNCC/MCT, Av. Getulio Vargas 333, Quitandinha, Petrópolis, RJ, 25651-070

Received: June 30, 2008

Revised: March 31, 2009

Published: August 2009

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Abstract

A one dimensional version of the dynamic Marguerre-Vlasov system in the presence of thermal effects is considered. The system depends on a parameter $\epsilon>0$ in a singular way as $\epsilon\to0$. Our interest is twofold: 1) To find the limit system as $\epsilon\to0$ and 2) To study the asymptotic behavior as $t\to+\infty$ of the total energy $E_{\epsilon}(t)$ and compare it with the total energy of the limit system.

Keywords:

singular limit,
uniform stabilization,
one-dimensional Marguerre-Vlasov system.

Mathematics Subject Classification: Primary: 35B40, 93D15.

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On the one-dimensional version of the dynamical Marguerre-Vlasov system with thermal effects

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