Skip to main content

Initial Boundary Value Problem for a Generalized Zakharov Equations

  • Conference paper
Book cover Theoretical and Mathematical Foundations of Computer Science (ICTMF 2011)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 164))

  • 1942 Accesses

Abstract

In this paper the authors consider the existence of the solution to the initial boundary value problem for a class of generalized Zakharov equations and prove the global existence of the generalized solution to the problem by a priori integral estimates and Galerkin method.

A Project Supported by Scientific Research Fund of Hunan Provincial Education Department No.10C1056, Hunan Natural Science Foundation Grant No.06JJ5013 and Scientific Research Found of Huaihua University No. HHUY2008-01.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Zakharov, V.E.: Collapse of Langmuir waves. Sov. Phys. JETP 35, 908–914 (1972)

    Google Scholar 

  2. Holmer, J.: Local ill-posedness of the 1D Zakharov system. Electron. J. Differential Equations 24, 1–24 (2007)

    MathSciNet  MATH  Google Scholar 

  3. Pecher, H.: An improved local well-posedness result for the one-dimensional Zakharov system. J. Math. Anal. Appl. 342, 1440–1454 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  4. Guo, B., Zhang, J., Pu, X.: On the existence and uniqueness of smooth solution for a generalized Zakharov equation. J. Math. Anal. Appl. 365, 238–253 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  5. Linares, F., Matheus, C.: Well Posedness for the 1D Zakharov-Rubenchik system. Advances in Differential Equations 14, 261–288 (2009)

    MathSciNet  MATH  Google Scholar 

  6. Linares, F., Saut, J.C.: The Cauchy problem for the 3D Zakharov-Kuznetsov equation. Discrete and Continuous Dynamical Systems 24, 547–565 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  7. You, S.: The posedness of the periodic initial value problem for generalized Zakharov equations. Nonlinear Analysis: Theory, Methods & Applications 71, 3571–3584 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  8. Masmoudi, N., Nakanishi, K.: From the Klein-Gordon-Zakharov system to the nonlinear Schroinger equation. J. Hyperbolic Differ. Equ. 2(4), 975–1008 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  9. Masmoudi, N., Nakanishi, K.: Energy convergence for singular limits of Zakharov type systems. Invent. Math. 172, 535–583 (2008)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2011 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

You, S., Ning, X. (2011). Initial Boundary Value Problem for a Generalized Zakharov Equations. In: Zhou, Q. (eds) Theoretical and Mathematical Foundations of Computer Science. ICTMF 2011. Communications in Computer and Information Science, vol 164. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-24999-0_11

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-24999-0_11

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-24998-3

  • Online ISBN: 978-3-642-24999-0

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics