Table of Contents Author Guidelines Submit a Manuscript
Journal of Applied Mathematics
Volume 2014, Article ID 897080, 9 pages
http://dx.doi.org/10.1155/2014/897080
Research Article

Optimal Polynomial Decay to Coupled Wave Equations and Its Numerical Properties

Department of Mathematics, Federal University of Para, Augusto Corrêa Street, 01, 66075-110 Belem, PA, Brazil

Received 28 November 2013; Revised 1 April 2014; Accepted 19 May 2014; Published 22 July 2014

Academic Editor: Roberto Barrio

Copyright © 2014 R. F. C. Lobato et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. M. Najafi, G. R. Sarhangi, and H. Wang, “The study of stability of coupled wave equations under various end conditions,” in Proceedings of 31st Conferences on Decision and Control, pp. 374–379, Tucson, Arizona, 1992.
  2. V. Komornik and B. Rao, “Boundary stabilization of compactly coupled wave equations,” Asymptotic Analysis, vol. 14, no. 4, pp. 339–359, 1997. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  3. F. Alabau Boussoira, “Stabilisation frontière indirecte de systèmes faiblement couplés,” Comptes Rendus de l'Académie des Sciences. Série I, vol. 328, no. 11, pp. 1015–1020, 1999. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  4. F. Alabau Boussoira, P. Cannarsa, and V. Komornik, “Indirect internal stabilization of weakly coupled evolution equations,” Journal of Evolution Equations, vol. 2, no. 2, pp. 127–150, 2002. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  5. M. L. Santos, M. P. C. Rocha, and S. C. Gomes, “Polynomial stability of a coupled system of wave equations weakly dissipative,” Applicable Analysis, vol. 86, no. 10, pp. 1293–1302, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  6. A. Borichev and Y. Tomilov, “Optimal polynomial decay of functions and operator semigroups,” Mathematische Annalen, vol. 347, no. 2, pp. 455–478, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  7. M. Najafi, “Study of exponential stability of coupled wave systems via distributed stabilizer,” International Journal of Mathematics and Mathematical Sciences, vol. 28, no. 8, pp. 479–491, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  8. A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations, Springer, New York, NY, USA, 1983. View at Publisher · View at Google Scholar · View at MathSciNet
  9. J. Prüss, “On the spectrum of C0-semigroups,” Transactions of the American Mathematical Society, vol. 284, no. 2, pp. 847–857, 1984. View at Publisher · View at Google Scholar · View at MathSciNet
  10. L. H. Fatori and J. E. M. Rivera, “Rates of decay to weak thermoelastic Bresse system,” IMA Journal of Applied Mathematics, vol. 75, no. 6, pp. 881–904, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  11. G. D. Smith, Numerical Solution of Partial Differential Equations: Finite Difference Methods, Oxford Applied Mathematics and Computing Science Series, 1984. View at MathSciNet
  12. M. Negreanu and E. Zuazua, “Uniform boundary controllability of a discrete 1-D wave equation,” Systems & Control Letters, vol. 48, no. 3-4, pp. 261–279, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  13. W. Strauss and L. Vazquez, “Numerical solution of a nonlinear Klein-Gordon equation,” Journal of Computational Physics, vol. 28, no. 2, pp. 271–278, 1978. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  14. L. N. Trefethen, Spectral Methods in MATLAB, SIAM, Philadelphia, Pa, USA, 2000. View at Publisher · View at Google Scholar · View at MathSciNet