Stabilization for viscous compressible heat-conducting media equations with nonmonotone state functions
[Stabilisation pour un milieu continu compressible avec pression non monotone]
Comptes Rendus. Mathématique, Tome 334 (2002) no. 2, pp. 119-124.

Nous étudions l'évolution 1d d'un milieu continu compressible conducteur de la chaleur. La pression est donnée par p(η,θ)=p0(η)+p1(η)θ, où p0 et p1 sont des fonctions non monotones assez générales pour permettre de traiter à la fois des modèles de fluides nucléaires et des solides thermo-visco-élastiques. Pour un problème aux limites d'évolution associé, avec grandes données, nous prouvons la stabilisation pour t→∞ au sens suivant : convergence ponctuelle et dans Lq pour le volume spécifique η, dans Lq pour la vitesse v, pour tout q∈[2,∞), et dans L2 pour la temperature θ.

We consider the system of quasilinear equations for 1d-motion of viscous compressible heat-conducting media. The state function has the form p(η,θ)=p0(η)+p1(η)θ, with general nonmonotone p0 and p1, which allows us to treat both nuclear fluids and thermoviscoelastic solids (for fluids, p, η, and θ are the pressure, specific volume, and temperature). For an initial boundary value problem with large data, we establish stabilization as t→∞: pointwise and in Lq for η, in Lq for v (the velocity), for any q∈[2,∞), and in L2 for θ.

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Accepté le :
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DOI : 10.1016/S1631-073X(02)02227-6
Ducomet, Bernard 1 ; Zlotnik, Alexander 2

1 CEA-Département de physique théorique et appliquée, BP 12, 91680 Bruyères le Châtel, France
2 MPEI–Department of Mathematical Modelling, Krasnokazarmennaja 14, 111250 Moscow, Russia
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Ducomet, Bernard; Zlotnik, Alexander. Stabilization for viscous compressible heat-conducting media equations with nonmonotone state functions. Comptes Rendus. Mathématique, Tome 334 (2002) no. 2, pp. 119-124. doi : 10.1016/S1631-073X(02)02227-6. http://www.numdam.org/articles/10.1016/S1631-073X(02)02227-6/

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