Addendum to: Qualitative aspects of solutions in resonators

• Autorzy: Quintanilla R. , Racke R.
• Języki publikacji: EN

Abstrakty

EN

In correcting a small mistake in [10], we can prove a new result on nonexponential stability for a coupled system arising in resonators. This also gives another (surprising and simple) example for a thermoelastic system changing from exponential stability to non-exponential stability, when changing from Fourier’s law to Cattaneo’s law in modeling of the heat conduction.

Słowa kluczowe

EN

hyperbolic model in thermoelasticity; well-posedness; exponential stability; Fourier law; Cattaneo law

• Wydawca: Instytut Podstawowych Problemów Techniki PAN
• Czasopismo: Archives of Mechanics
• Rocznik: 2011
• Tom: Vol. 63, nr 4
• Strony: 429--435
• Opis fizyczny: Bibliogr. 10 poz.

Twórcy

autor

Quintanilla R.

autor

Racke R.

• Department of Applied Mathematics II UPC Terrassa, Colom 11, 08222 Terrassa, Spain,

Bibliografia

• 1. G. Avalos, I. Lasiecka, Exponential stability of a thermoelastic system without mechanical dissipation, Rend. Instit. Mat. Univ. Trieste Suppl., 28, 1–28, 1997.
• 2. H. Fernández Sare, R. Racke, On the stability of damped Timoshenko systems –Cattaneo versus Fourier law, Arch. Rational Mech. Anal., 194, 221–251, 2009. Addendum to: Qualitative aspects of solutions in resonators 435
• 3. J.U. Kim, On the energy decay of a linear thermoelastic bar and plate, SIAM J. Math. Anal., 23, 889–899, 1992.
• 4. I. Lasiecka, R. Triggiani, Two direct proofs on the analyticity of the S.C. semigroup arising in abstract thermoelastic equations, Adv. Differential Equations, 3, 387–416, 1998.
• 5. I. Lasiecka, R. Triggiani, Analyticity, and lack thereof, of thermo-elastic semigroups, ESAIM, Proc., 4, 199–222, 1998.
• 6. I. Lasiecka, R. Triggiani, Analyticity of thermo-elastic semigroups with coupled hinged/Neumann boundary conditions, Abstract Appl. Anal., 3, 153–169, 1998.
• 7. I. Lasiecka, R. Triggiani, Analyticity of thermo-elastic semigroups with free Bondary conditions, Annali Scuola Norm. Sup. Pisa, 27, 457–482, 1998.
• 8. Z. Liu, S. Zheng, Exponential stability of the Kirchhoff plate with thermal or viscoelastic damping, Quart. Appl. Math., 53, 551–564, 1997.
• 9. J.E. Muñoz Rivera, R. Racke, Smoothing properties, decay and global existence of solutions to nonlinear coupled systems of thermoelastic type, SIAM J. Math. Anal., 26, 1547–1563, 1995.
• 10. R. Quintanilla, R. Racke, Qualitative aspects in resonators, Arch. Mech., 60, 345–360, 2008.