Skip to main content
Log in

Exponential Decay for the Solutions of Wave Equations of Kirchhoff Type with Strong Damping

  • Published:
Acta Mathematica Hungarica Aims and scope Submit manuscript

Abstract

We study some decay estimates of the energy of the following nonlinear problem of Kirchhoff type:.....

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. M. M. Cavalcanti, V. N. Domingos Cavalcanti, J. S. Prates Filho and J. A. Soriano, Existence and exponential decay for a Kirchhoff-Carrier model with viscosity, J. Math. Anal. Appl., 226 (1998), 40–60.

    Google Scholar 

  2. G. Chen, Energy decay estimates and exact boundary value controllability for the wave equation in a bounded domain, J. Math. Pures Appl., 58 (1979), 249–273.

    Google Scholar 

  3. G. C. Gorain, Exponential energy decay estimate for the solutions of internally damped wave equation in a bounded domain, J. Math. Anal. Appl., 216 (1997), 510–520.

    Google Scholar 

  4. V. Komornik and E. Zuazua, A direct method for boundary stabilization of the wave equation, J. Math. Pures Appl., 69 (1990), 33–54.

    Google Scholar 

  5. I. Lasiecka and D. Tataru, Uniform boundary stabilization of semilinear wave equations with nonlinear boundary damping, Differential Integral Equations, 6 (1993), 507–533.

    Google Scholar 

  6. J. E. Lions, On some questions in boundary value problems of mathematical physics, in International Symposium on Continuum Mechanics and Partial Differential Equations (Rio de Janeiro, 1977), North-Holland (Amsterdam, 1978).

    Google Scholar 

  7. L. A. Medeiuros and M. Milla Miranda, On a nonlinear wave equation with damping, Rev. Mat. Univ. Complut. Madrid, 3 (1990), 613–627.

    Google Scholar 

  8. J. Y. Park and I. H. Jung, On a class of quasilinear hyperbolic equations and Yosida approximations, Indian J. Pure Appl. Math., 30 (1999), 1091–1106.

    Google Scholar 

  9. J. Y. Park, I. H. Jung and Y. H. Kang, Some quasilinear hyperbolic equations and Yosida approximations, to appear in Bull. Korean Math. Soc.

  10. J. Quinn and D. L. Russel, Asymptotic stability and energy decay for solutions of hyperbolic equations with boundary damping, Proc. Roy. Soc. Edinburgh, Sect. A, 77 (1977), 97–127.

    Google Scholar 

  11. C. F. Vasconcellos and L. M. Teixeira, Strong solutions and exponential decay for a nonlinear hyperbolic equation, Appl. Anal., 51 (1993), 155–173.

    Google Scholar 

  12. E. Zuazua, Stability and decay for a class of nonlinear hyperbolic problems, Asymptotic Anal., 1 (1988), 161–185.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Il Hyo, J., Yong-Hoon, L. Exponential Decay for the Solutions of Wave Equations of Kirchhoff Type with Strong Damping. Acta Mathematica Hungarica 92, 163–170 (2001). https://doi.org/10.1023/A:1013768414495

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1013768414495

Keywords

Navigation