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

Olivier Glass (1)

1 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision

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.

Mots clés: Contrôlabilité; systèmes hyperboliques de lois de conservation

Domaines: Optimisation et contrôle [math.OC]; Equations aux dérivées partielles [math.AP]

Olivier Glass. On the controllability of the non-isentropic 1-D Euler equation. Journal of Differential Equations, 2014, Volume 257 (Issue 3), pp.10.1016/j.jde.2014.04.013. ⟨hal-00813700⟩