Skip to main content
Log in

Energy decay for the quasilinear wave equation with viscosity

  • Published:
Mathematische Zeitschrift Aims and scope Submit manuscript

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

Access this article

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

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

Instant access to the full article PDF.

References

  1. Alikakos, N., Rostamian, R.: Gradient estimates for degenerate diffusion equations, I, Math. Annalen259, 53–70 (1982)

    Article  MATH  MathSciNet  Google Scholar 

  2. Ebihara, Y.: On some nonlinear evolution equations with the strong dissipation, J. Differential Equations30, 149–164 (1978)

    Article  MATH  MathSciNet  Google Scholar 

  3. Greenberg, J.: On the existence, uniquencess, and stability of solutions of the equations ρ0 X tt =E(X) x X xx +iX xtx , J. Math. Anal. Appl.25, 575–591 (1969)

    Article  MATH  MathSciNet  Google Scholar 

  4. Greenberg, J., MacCamy, R., and Mizel, V., On the existence, uniqueness and stability of solutions of the equation σ′(u x )u xx +λu xtx 0 u tt , J. Math. Mech.17, 707–728 (1968)

    MATH  MathSciNet  Google Scholar 

  5. Kawashima, S., and Shibata, Y.: Global existence and exponential stability of small solutions to nonlinear viscoelasticity, Comm. Math. Phys.148, 189–208 (1992)

    Article  MATH  MathSciNet  Google Scholar 

  6. Kobayashi, T., Pecher, H., and Shibata, Y.: On a global in time existence theorem of smooth solutions to nonlinear wave equation with viscosity, Math. Annalen.296, 215–234 (1993)

    Article  MATH  MathSciNet  Google Scholar 

  7. Nakao, M.: Asymptotic stability of the bounded or almost periodic solutions of the wave equation with nonlinear dissipative terms, J. Math. Anal. Appl.58, 368–386 (1977)

    Article  MathSciNet  Google Scholar 

  8. Nakao, M.: A difference inequality and its applications to nonlinear evolution equations, J. Math. Soc. Japan30, 747–762 (1978)

    Article  MATH  MathSciNet  Google Scholar 

  9. Nakao, M.: Decay of solutions of some nonlinear evolutions, J. Math. Anal. Appl.60, 542–549 (1977)

    Article  MATH  MathSciNet  Google Scholar 

  10. Nakao, M.: On global classical solutions of a quasilinear wave equation with a viscoelastic term, Math. Rep., Kyushu Univ.13, 1–29 (1981)

    MATH  MathSciNet  Google Scholar 

  11. Webb, G.: Existence and asymptotic behavior for a strongly damped nonlinear wave equation, Canad. J. Math.32, 61–643 (1980)

    MathSciNet  Google Scholar 

  12. Yamada, Y.: Some remarks on the equationy u (y x )y xx -y xtx =f, Osaka J. Math.17, 303–323 (1980)

    MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Nakao, M. Energy decay for the quasilinear wave equation with viscosity. Math Z 219, 289–299 (1995). https://doi.org/10.1007/BF02572366

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02572366

Keywords

Navigation