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We study the problem of exponential decaying for solutions of porousthermoelasticity system, when time (…). For suficiently small values of the parameter of intensity of elasticity-porosity interactions the exponential decaying is established. In the considerations we apply the idea of compact decoupling for the system of equations. The exponential decaying property is proved first for the corresponding decoupled system, which is simpler to handle, then the property is derived for the original system.
Wydawca
Czasopismo
Rocznik
Tom
Strony
847--868
Opis fizyczny
Bibliogr. 15 poz.
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autor
autor
- Institute Of Mathematics And Physics University Of Technology And Life Sciences Ul. Kaliskiego 7 85-796 Bydgoszcz, Poland, glowip@gmail.com
Bibliografia
- [1] F.Alabau, V.Komornik, Boundary observability, controllability and stabilization of linear elastodynamic systems SIAM J.Control Optim.37(2)(1998), 521-542.
- [2] N.Burq, G.Lebeau, Measures de defaut de compacte, application au systeme de Lame Ann. Sci. Ecole Norm. Sup. (4)34(6) (2001), 817-870.
- [3] J.Cheng ,V.Isakov, M.Yamamoto, Qi Zhou, Lipschitz stability in lateral Cauchy problem for elasticity system J.Math. Kyoto Univ. 43(3) (2003), 475-501.
- [4] S.C.Cowin, J.W.Nunziato, Linear elastic materials with voids J.Elasticity 13 (1983), 125-147.
- [5] R.Dautray, J.L.Lions Mathematical Analysis and Numerical Methods for Science and Technology v.3, Spectral Theory and Applications, Springer, 2000.
- [6] R.Dautray, J.L.Lions Mathematical Analysis and Numerical Methods for Science and Technology v.5, Evolution Problems I, Springer, 2000.
- [7] P.Głowiński, A.Łada, Stabilization of elasticity-viscoporosity system by linear boundary feedback Math. Methods Appl. Sci.32 (2009), 702-722.
- [8] P.Głowiński, A.Łada, Asymtotic stability of solutions to the equations of linear elasticity and thermoelasticity in viscoporous media Demonstratio Math. 42 (2009), 754-779.
- [9] Bao Zhu Guo, On the exponential stability of c 0-semigroups on Banach spaces with compact perturbations Semigroup Forum 59 (1999), 190-196.
- [10] D.Henry, O.Lopes, A.Perissinitto, On the essential spectrum of a semigroup of thermoelasticity Nonlinear Anal.21 (1993), 65-75.
- [11] G.Lebeau, E.Zuazua, Decay rates for the three-dimensional linear system of thermoelasticity Arch. Ration. Mech. Anal. 148 (1999), 179-231.
- [12] A.Magana, R.Quintanilla, On the times decay of solutions in one-dimensional theories of porous materials Internat. J.Solids Structures 43 (2006), 3414-3427.
- [13] W.McLean, Strongly Elliptic Systems and Boundary Integral Equations Cambridge Univ. Press, Cambridge, 2000.
- [14] A.Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations Applied Mathematical Sciences 44, Springer, 1983.
- [15] E.Zuazua, Controllability of the linear system of theormoelasticity J.Math. Pures et Appl.74 (1995), 291-315.
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Bibliografia
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bwmeta1.element.baztech-article-PWA4-0035-0028