Advances in Differential Equations

On the asymptotic behaviour of a one-dimensional monocharged plasma and a rescaling method

Jürgen Batt, Markus Kunze, and Gerhard Rein

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We consider a one-dimensional, monocharged plasma as described by the Vlasov--Poisson system and investigate the behaviour of the solutions for large times. Using a rescaling method we are able to determine an explicit solution of the system which corresponds to a globally attractive steady state for the rescaled system. We investigate in which sense and at which rate the solutions of the rescaled system converge to this global attractor and interpret the results for the original system.

Article information

Adv. Differential Equations, Volume 3, Number 2 (1998), 271-292.

First available in Project Euclid: 19 April 2013

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 82D10: Plasmas
Secondary: 35B40: Asymptotic behavior of solutions 35Q99: None of the above, but in this section 45K05: Integro-partial differential equations [See also 34K30, 35R09, 35R10, 47G20] 76X05: Ionized gas flow in electromagnetic fields; plasmic flow [See also 82D10]


Batt, Jürgen; Kunze, Markus; Rein, Gerhard. On the asymptotic behaviour of a one-dimensional monocharged plasma and a rescaling method. Adv. Differential Equations 3 (1998), no. 2, 271--292.

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