Skip to main content
SpringerLink
Log in

Maximal Attractors for the Klein-Gordon-Schrödinger Equation in Unbounded Domain

  • Published:
Acta Applicandae Mathematicae Aims and scope Submit manuscript

Abstract

In this paper, we study the behavior of solutions for the Klein-Gordon-Schrödinger equation in the whole space ℝ. We first prove the continuity of the solutions on initial data and then establish the asymptotic smoothness of solutions. Finally, we show the existence of the maximal attractor.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Bachelot, A.: Probleme de Cauchy pour des systems hyperboliques semi-lineaires. Ann. Inst. Henri Poincaré Anal. Non Linéaire 1, 453–478 (1984)

    MATH  MathSciNet  Google Scholar 

  2. Ball, J.M.: Continuity properties and global attractors of generalized semiflows and Navier-Stokes equations. J. Nonlinear Sci. 7, 475–502 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  3. Biler, P.: Attractors for the system of Schrödinger and Klein-Gordon equations with Yukawa coupling. SIAM J. Math. Anal. 21, 1190–1212 (1990)

    Article  MATH  MathSciNet  Google Scholar 

  4. Boling, G., Yongsheng, L.: Attractor for dissipative Klein-Gordon-Schrödinger equations in \({\Bbb{R}}^{3}\) . J. Differ. Equ. 136, 356–377 (1997)

    Article  MATH  Google Scholar 

  5. Feireisl, E.: Attractors for semilinear damped wave equations on \({\Bbb{R}}^{3}\) . Nonlinear Anal. 23, 187–195 (1994)

    Article  MATH  MathSciNet  Google Scholar 

  6. Fukuda, I., Tsutsumi, M.: On coupled Klein-Gordon-Schrödinger equations II. J. Math. Anal. Appl. 66, 358–378 (1978)

    Article  MATH  MathSciNet  Google Scholar 

  7. Fukuda, I., Tsutsumi, M.: On coupled Klein-Gordon-Schrödinger equations III. Math. Jpn. 24, 307–321 (1979)

    MATH  MathSciNet  Google Scholar 

  8. Guo, B., Li, Y.: Attractor for Klein-Gordon-Schrödinger equations in \({\Bbb{R}}^{3}\) . J. Differ. Equ. 136, 356–377 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  9. Hale, J.K.: Asymptotic Behavior of Dissipative Systems. Math. Surveys and Monographs, vol. 25. Am. Math. Soc., Providence (1988)

    MATH  Google Scholar 

  10. Hayashi, N., von Wahl, W.: On the global strong solutions of coupled Klein-Gordon-Schrödinger equations. J. Math. Soc. Jpn. 39, 489–497 (1987)

    Article  MATH  Google Scholar 

  11. Karachalios, N.I., Stavrakakis, N.M.: Global attractor for the weakly damped driven Schrödinger equation in \(H^{2}(\Bbb{R})\) . Nonlinear Differ. Equ. Appl. 9, 347–360 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  12. Li, Y.: Finite dimension of global attractor for weakly dissipative Klein-Gordon-Schrödinger equations. Preprint

  13. Yongsheng, L.: Finite dimension of global attractor for weakly dissipative Klein-Gordon-Schrödinger equations. Preprint

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, College of Science, Pusan National University, Kumjung, Pusan, 609-735, Republic of Korea

    Jong Yeoul Park

  2. National Institute for Mathematical Sciences, 385-16, Doryong-dong, Yuseong-gu, Daejeon, 305-340, Korea

    Jung Ae Kim

Authors
  1. Jong Yeoul Park
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jung Ae Kim
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jung Ae Kim.

Additional information

This work was supported by the National Institute for Mathematical Sciences.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Park, J.Y., Kim, J.A. Maximal Attractors for the Klein-Gordon-Schrödinger Equation in Unbounded Domain. Acta Appl Math 108, 197–213 (2009). https://doi.org/10.1007/s10440-008-9309-0

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10440-008-9309-0

Keywords

Search

Navigation