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

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2009, 2009(Special): 536-547. doi: 10.3934/proc.2009.2009.536

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

Gustavo Alberto Perla Menzala ^1, and Julian Moises Sejje Suárez ^1,

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

Received July 2008 Revised April 2009 Published September 2009

Abstract
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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.

Citation: Gustavo Alberto Perla Menzala, Julian Moises Sejje Suárez. On the one-dimensional version of the dynamical Marguerre-Vlasov system with thermal effects. Conference Publications, 2009, 2009 (Special) : 536-547. doi: 10.3934/proc.2009.2009.536

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