[Stabilization of a system of anisotropic thermoelasticity by nonlinear feedbacks.]
In this Note we study the stabilization of an anisotropic thermoelasticity system with (natural) Neumann boundary condition and nonlinear internal and/or boundary feedbacks. Our method consists of showing the exponential stability of the linear system by using an integral inequality, obtained by the technique of Bey et al. [E.J.D.E. 78 (2001) 1–23]; the stabilisation of the nonlinear system is deduced owing to the results from Nicaise [Rendiconti Di Matematica, Ser. VII 23 (2003) 83–116].
Dans cette Note on étudie la stabilisation d'un système de la thermoélasticité anisotrope linéaire avec condition (naturelle) de Neumann sur une partie du bord, à l'aide de feedbacks non linéaires, l'un interne et/ou l'autre frontière. La démarche utilisée consiste à montrer la stabilisation exponentielle du système linéaire en établissant une inégalité intégrale, obtenue par la technique de Bey et al. [E.J.D.E. 78 (2001) 1–23] ; la stabilisation du système non linéaire s'en déduit grâce aux résultats de Nicaise [Rendiconti Di Matematica, Ser. VII 23 (2003) 83–116].
Accepted:
Published online:
Amar Heminna 1; Serge Nicaise 2; Abdoulaye Sene 3
@article{CRMATH_2004__339_8_561_0,
author = {Amar Heminna and Serge Nicaise and Abdoulaye Sene},
title = {Stabilisation d'un syst\`eme de la thermo\'elasticit\'e anisotrope avec feedbacks non lin\'eaires},
journal = {Comptes Rendus. Math\'ematique},
pages = {561--566},
publisher = {Elsevier},
volume = {339},
number = {8},
year = {2004},
doi = {10.1016/j.crma.2004.08.008},
language = {fr},
}
TY - JOUR AU - Amar Heminna AU - Serge Nicaise AU - Abdoulaye Sene TI - Stabilisation d'un système de la thermoélasticité anisotrope avec feedbacks non linéaires JO - Comptes Rendus. Mathématique PY - 2004 SP - 561 EP - 566 VL - 339 IS - 8 PB - Elsevier DO - 10.1016/j.crma.2004.08.008 LA - fr ID - CRMATH_2004__339_8_561_0 ER -
%0 Journal Article %A Amar Heminna %A Serge Nicaise %A Abdoulaye Sene %T Stabilisation d'un système de la thermoélasticité anisotrope avec feedbacks non linéaires %J Comptes Rendus. Mathématique %D 2004 %P 561-566 %V 339 %N 8 %I Elsevier %R 10.1016/j.crma.2004.08.008 %G fr %F CRMATH_2004__339_8_561_0
Amar Heminna; Serge Nicaise; Abdoulaye Sene. Stabilisation d'un système de la thermoélasticité anisotrope avec feedbacks non linéaires. Comptes Rendus. Mathématique, Volume 339 (2004) no. 8, pp. 561-566. doi : 10.1016/j.crma.2004.08.008. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2004.08.008/
[1] Boundary observability, controllability and stabilization of linear elastodynamic systems, SIAM J. Contr. Optim., Volume 37 (1999), pp. 521-542
[2] Boundary stabilization of a linear elastodynamic system with variables coefficients, E.J.D.E., Volume 78 (2001), pp. 1-23
[3] Stabilisation frontière du système élastodynamique dans un polygone plan, C. R. Acad. Sci. Paris, Ser. I, Volume 338 (2004), pp. 213-218
[4] Implications of sharp trace regularity results on boundary stabilization of the system of linear elasticity, J. Math. Anal. Appl., Volume 223 (1998), pp. 126-150
[5] Exact Controllability and Stabilisation, The Multiplier Method, RMA, Masson, 1994
[6] Boundary stabilization of linear elastodynamic systems, SIAM J. Contr. Optim., Volume 21 (1983), pp. 968-984
[7] Partial exact controllability and exponential stability in higher-dimensional linear thermoelasticity, ESAIM COCV, Volume 3 (1998), pp. 23-48
[8] Decay rates for the three-dimensional linear system of thermoelasticity, Arch. Rational Mech. Anal., Volume 148 (1999), pp. 179-231
[9] Uniform Stabilization of the higher dimentional System of thermoelasticity with a nonlinear boundary feedback, Quart. Appl. Math., Volume 59 (2001), pp. 269-314
[10] Stability and controllability of and abstract evolution equetion of hyperbolic type and concrete applications, Rendiconti Di Matematica, Ser. VII, Volume 23 (2003), pp. 83-116
[11] Stability and controllability of the electromagneto-elastic system, Portugal. Math., Volume 60 (2003), pp. 37-70
Cited by Sources:
Comments - Policy