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On the controllability of the non-isentropic 1-D Euler equation

Glass, Olivier (2014), On the controllability of the non-isentropic 1-D Euler equation, Journal of Differential Equations, 257, 3, p. 638-719. http://dx.doi.org/10.1016/j.jde.2014.04.013

Type
Article accepté pour publication ou publié
External document link
http://hal.archives-ouvertes.fr/hal-00813700
Date
2014
Journal name
Journal of Differential Equations
Volume
257
Number
3
Publisher
Elsevier
Pages
638-719
Publication identifier
http://dx.doi.org/10.1016/j.jde.2014.04.013
Metadata
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Author(s)
Glass, Olivier
Abstract (EN)
In this paper, we examine the question of the boundary controllability of the one-dimensional non-isentropic Euler equation for compressible polytropic gas, in the context of weak entropy solutions. We consider the system in Eulerian coordinates and the one in Lagrangian coordinates. We obtain for both systems a result of controllability toward constant states (with the limitation $\gamma < \frac{5}{3}$ on the adiabatic constant for the Lagrangian system). The solutions that we obtain remain of small total variation in space if the initial condition is itself of sufficiently small total variation.
Subjects / Keywords
hyperbolic systems of conservation laws; non-isentropic Euler equations; Controllability; systèmes hyperboliques de lois de conservation; Contrôlabilité

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