Skip to main content
Log in

Exact boundary controllability for higher order quasilinear hyperbolic equations

  • Published:
Applied Mathematics-A Journal of Chinese Universities Aims and scope Submit manuscript

Abstract

By means of the existence and uniqueness of semi-global C 1 solution to the mixed initial-boundary value problem with general nonlinear boundary conditions for first order quasilinear hyperbolic systems with zero eigenvalues, the local exact boundary controllability for higher order quasilinear hyperbolic equations is established.

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. Cui Zefen, Zhou Hongmo, Xie Qinglan. Boundary value problem for higher order hyperbolic equation in two independent variables, Acta Sc Nat Univ Fudan, 1966, 11(1):29–40.

    Google Scholar 

  2. Cirinà M. Nonlinear hyperbolic problems with solutions on preassigned sets, Michigan Math J, 1970, 17:193–209.

    Article  MATH  Google Scholar 

  3. Li Tatsien, Jin Yi. Semi-global C 1 solution to the mixed initial-boundary value problem for quasilinear hyperbolic systems, Chin Ann Math Ser B, 2001, 22:325–336.

    Article  MATH  Google Scholar 

  4. Li Tatsien, Jin Yi, Semi-global C 1 solution to the mixed initial-boundary value problem for quasilinear hyperbolic systems, Chin Ann Math Ser B, 2001, 22:325–336.

    Article  MATH  Google Scholar 

  5. Li Tatsien, Rao Bopeng. Exact boundary controllability for quasilinear hyperbolic systems, SIAM J Control Optim, 2003, 41:1748–1755.

    Article  Google Scholar 

  6. Li Tatsien, Rao Bopeng, Jin Yi. Solution C 1 semi-globale et contrôlabilité exacte frontière de systèmes hyperboliques quasi linéaires. C R Acad Sci Paris, Ser I, 2001, 333:219–224.

    MATH  Google Scholar 

  7. Li Tatsien, Rao Bopeng. Local exact boundary controllability for a class of quasilinear hyperbolic systems, Chin Ann Math Ser B, 2002, 23:209–218.

    Article  MATH  Google Scholar 

  8. Li Tatsien, Yu Lixin. Exact controllability for first order quasilinear hyperbolic systems with zero eigenvalues, Chin Ann Math Ser B, 2003, 24:415–422.

    Article  MATH  Google Scholar 

  9. Li Tatsien, Yu Lixin. Contrôlabilité exacte frontière pour les équations des ondes quasilinéaires unidimensionnelles, C R Acad Sci Paris Ser I, 2003, 337:271–276.

    MATH  Google Scholar 

  10. Li Tatsien, Yu Lixin. Exact boundary controllability for 1-D quasilinear wave equations, to appear.

  11. Yu Lixin. Semi-global C 1 solution to the mixed initial-boundary value problem for a general class of quasilinear hyperbolic systems (in Chinese), Chin Ann Math Ser A, 2004, 25:549–560.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

Recommended by Li Daqian.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Lixin, Y. Exact boundary controllability for higher order quasilinear hyperbolic equations. Appl. Math. Chin. Univ. 20, 127–141 (2005). https://doi.org/10.1007/s11766-005-0045-1

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11766-005-0045-1

MR Subject Classification

Keywords

Navigation