PL EN


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
Tytuł artykułu

Asymtotic stability of solutions to the equations of linear elasticity and thermoelasticity in viscoporus media

Wybrane pełne teksty z tego czasopisma
Identyfikatory
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
The systems of evolution equations modelling elasticity and thermoelas-ticity of viscoporous bounded media are considered. The existence of co-semigroups of contractions defining solutions to the systems is proved. The asymptotic vanishing of energies of solutions when t -> (infinity) is explained.
Słowa kluczowe
Wydawca
Rocznik
Strony
757--779
Opis fizyczny
Bibliogr. 21 poz.
Twórcy
autor
  • Institute of Mathematcis University of Technology and Life Sciences ul. Kaliskiego 7, 85-796 Bydgoszcz, Poland, a.lada@utp.edu.pl
Bibliografia
  • [1] F. Alabau, P. Cannarsa, V. Komornik, Indirect internal stabilization of weakly coupled evolution equations, J. Evolution Equations (2) 2002, 127-150.
  • [2] P. S. Casas, R. Quintanilla, Exponential decay in one-dimensional porous-thermoelasticity, Mech. Res. Comm. (32) 2005, 652-658.
  • [3] M. Ciarletta, D. Iesan, Non-classical Elastic Solids, Pitman Research Notes in Mathematics Series, vol 293, Longman Scientific and Technical, Harlow; JohnWiley&Sons, New York, 1993
  • [4] S. C. Cowin, J. W. Nunziato, Linear elastic materials with voids, J. Elasticity 13 (1983), 125-147.
  • [5] C. M. Dafermos, On the existence and the asymptotic stability of solutions to the equations of linear thermoelasticity, Arch. Rational Mech. Anal. 29 (1968), 241-271 .
  • [6] R. Dager, E. Zuazua, Wave Propagation, Observation and Control in 1-d Flexible Multi-structures, Math. Appl. 50, 2006.
  • [7] R. Dautray, J. L. Lions, Mathematical Analysis and Numerical Methods for Sciences and Technology, v5, Evolution Problems I, Springer-Verlag, Berlin, 1992
  • [8] P. Głowiński, A. Łada, Stabilization of elasticity-viscoporosity system by linear boundary feedback, Math. Methods Appl. Sci. 32 (2009), 702-722.
  • [9] R. Grot, Thermodynamics of continuum with microstructure, Internat. J. Engrg. Sci. 7 (1969), 801-814
  • [10] D. Henry, O. Lopes, A. Perissinitto, On the essential spectrum of a semigroup of thermoelasticity, Nonlinear Anal. 21 (1993), 65-75.
  • [11] D. Iesan, Thermoelastic Models of Continua, Springer, Berlin, 2004.
  • [12] S. Jiang, R. Racke, Evolution Equationsin Thermoelasticity, Chapman and Hall ICRC, Boca Raton, 2000.
  • [13] H. Koch, Mixed problems for fully nonlinear hyperbolic equations, Math. Z. 214 (1993), 9-42.
  • [14] G. Lebeau, E. Zuazua, Decay rates for the three-dimensional linear system of thermoelasticity, ARMA 148 (1999), 179-231.
  • [15] M. C. Leseduarte, R. Quintanilla, Instability, nonexistence and uniqueness in elasticity with porous dissipation, Differential Equations and Nonlinear Mechanics (2006), 1-14.
  • [16] K. Liu, Locally distributed control and damping for the conservative systems, SIAM J. Control Optim. 35(5) (1997), 1547-1590.
  • [17] A. Magana, R. Quintanilla, On the exponential decay of solutions in one-dimensional generalized of porous-thermo-elasticity, Asymptotic Analysis 49 (2006), 173-187.
  • [18] A. Magana, R. Quintanilla, On the time decay of solutions in one-dimensional theories of porous materials, Internat. J. Solids and Structures 43 (2006), 3414-3427.
  • [19] W. McLean, Strongly Elliptic Systems and Boundary Integral Equations, Cambridge University Press, 2000.
  • [20] A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations, Appl. Math. Sci. 44, Springer-Verlag, 1983.
  • [21] Y. Tomilov, A resolvent approach to stability of operator semigroups, J. Operator Theory 46 (2001), 63-98.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-PWA5-0027-0009
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.