Free access
Issue
ESAIM: M2AN
Volume 36, Number 4, July/August 2002
Page(s) 657 - 691
DOI http://dx.doi.org/10.1051/m2an:2002029
Published online 15 September 2002
  1. J.M. Ball, Initial-boundary value problems for an extensible beam. J. Math. Anal. Appl. 41 (1973) 69-90.
  2. Ph. Ciarlet, Mathematical elasticity, Vol. II. Theory of plates. Stud. Math. Appl. 27 (1997).
  3. A. Cimetière, G. Geymonat, H. Le Dret, A. Raoult and Z. Tutek, Asymptotic theory and analysis for displacements and stress distribution in nonlinear elastic straight slender rods. J. Elasticity 19 (1988) 111-161. [CrossRef] [MathSciNet]
  4. R.W. Dickey, Free vibrations and dynamic buckling of the extensible beam. J. Math. Anal. Appl. 29 (1970) 443-454. [CrossRef] [MathSciNet]
  5. A. Haraux and E. Zuazua, Decay estimates for some damped hyperbolic equations. Arch. Rational Mech. Anal. 100 (1998) 191-206. [CrossRef] [MathSciNet]
  6. V.A. Kondratiev and O.A. Oleinik, Hardy's and Korn's type inequalities and their applications. Rendiconti di Matematica VII (1990) 641-666.
  7. V. Komornik and E. Zuazua, A direct method for the boundary stabilization of the wave equation. J. Math. Pures Appl. (9) 69 (1990) 33-55. [MathSciNet]
  8. J.E. Lagnese, Boundary stabilization of thin plates. SIAM Stud. Appl. Math., Philadelphia (1989).
  9. J.E. Lagnese, Recent progress in exact boundary controllability and uniform stability of thin beams and plates. Lect. Notes in Pure and Appl. Math. 128, Dekker, New York (1991) 61-111.
  10. I. Lasiecka, Weak, classical and intermediate solutions to full von Kármán system of dynamic nonlinear elasticity. Appl. Anal. 68 (1998) 121-145. [MathSciNet]
  11. J.E. Lagnese and G. Leugering, Uniform stabilization of a nonlinear beam by nonlinear boundary feedback. J. Differential Equations 91 (1991) 355-388. [CrossRef] [MathSciNet]
  12. J.L. Lions, Perturbations singulières dans les problèmes aux limites et contrôle optimal. Springer-Verlag, Berlin, in Lectures Notes in Math. 323 (1973).
  13. A.H. Nayfeh and D.T. Mook, Nonlinear oscillations. Wiley-Interscience, New York (1989).
  14. A.F. Pazoto and G.P. Menzala, Uniform stabilization of a nonlinear beam model with thermal effects and nonlinear boundary dissipation. Funkcial. Ekvac. 43 (2000) 339-360. [MathSciNet]
  15. J.P. Puel and M. Tucsnak, Boundary stabilization for the von Karman equations. SIAM J. Control Optim. 33 (1995) 255-273
  16. J.P. Puel and M. Tucsnak, Global existence of the full von Kármán system. Appl. Math. Optim. 34 (1996) 139-160. [CrossRef] [MathSciNet]
  17. G.P. Menzala and E. Zuazua, The beam equation as a limit of 1-D nonlinear von Kármán model. Appl. Math. Lett. 12 (1999) 47-52. [CrossRef] [MathSciNet]
  18. G.P. Menzala and E. Zuazua, Timoshenko's beam equation as limit of a nonlinear one-dimensional von Kármán system. Proc. Roy. Soc. Edinburg Sect. A 130 (2000) 855-875. [CrossRef]
  19. G.P. Menzala and E. Zuazua, Timoshenko's plate equation as a singular limit of the dynamical von Kármán system. J. Math. Pures Appl. (9) 79 (2000) 73-94. [CrossRef] [MathSciNet]
  20. V.I. Sedenko, On the uniqueness theorem for generalized solutions of initial-boundary problems for the Marguerre-Vlasov vibrations of shallow shells with clamped boundary conditions. Appl. Math. Optim. 39 (1999) 309-326. [CrossRef] [MathSciNet]
  21. J. Simon, Compact sets in the space Lp(0,T;B). Ann. Mat. Pura Appl. (4) CXLVI (1987) 65-96.
  22. L. Trabucho de Campos and J. Via no, Mathematical modelling of rods. Handbook of numerical analysis, Vol. IV, North Holland, Amsterdam (1996) 487-974.
  23. E. Zuazua, Stability and decay for a class of nonlinear hyperbolic problems. Asymptot. Anal. 1 (1988) 1-28.

Recommended for you