Skip to main content
SpringerLink
Log in

On the asymptotics of solutions to the second initial boundary value problem for Schrödinger systems in domains with conical points

  • Published:
Applications of Mathematics Aims and scope Submit manuscript

Abstract

In this paper, for the second initial boundary value problem for Schrödinger systems, we obtain a performance of generalized solutions in a neighborhood of conical points on the boundary of the base of infinite cylinders. The main result are asymptotic formulas for generalized solutions in case the associated spectrum problem has more than one eigenvalue in the strip considered.

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. N.T. Anh, N.M. Hung: Asymptotic formulas for solutions of parameter-depending elliptic boundary-value problems in domains with conical points. Electron. J. Differ. Equ. No. 125 (2009), 1–21.

  2. N.M. Hung: The first initial boundary value problem for Schrödinger systems in non-smooth domains. Diff. Uravn. 34 (1998), 1546–1556. (In Russian.)

    Google Scholar 

  3. N.M. Hung, N.T. Anh: Regularity of solutions of initial-boundary value problems for parabolic equations in domains with conical points. J. Differ. Equations 245 (2008), 1801–1818.

    Article  MathSciNet  MATH  Google Scholar 

  4. N.M. Hung, J.C. Yao: On the asymptotics of solutions of the first initial boundary value problem for hyperbolic systems in infinite cylinders with base containing conical points. Nonlinear Anal., Theory, Methods Appl. 71 (2009), 1620–1635.

    Article  MathSciNet  MATH  Google Scholar 

  5. N.M. Hung, N.T.K. Son: Existence and smoothness of solutions to second initial boundary value problems for Schrödinger systems in cylinders with non-smooth base. Electron. J. Differ. Equ., No. 35 (2008), 1–11.

  6. N.M. Hung, N.T.M. Son: On the regularity of solution of the second initial boundary value problem for Schrödinger systems in domains with conical points. Taiwanese J. Math. 13 (2009), 1885–1907.

    MathSciNet  MATH  Google Scholar 

  7. N.M. Hung, T.X. Tiep, N.T.K. Son: Cauchy-Neumann problem for second-order general Schrödinger equations in cylinders with non-smooth bases. Bound. Value Probl., Vol. 2009, Article ID 231802 (2009), 1–13.

    Google Scholar 

  8. T. Kato: Perturbation Theory for Linear Operators. Springer, Berlin, 1966.

    MATH  Google Scholar 

  9. A. Kokotov, B.A. Plamenevskiĭ: On the asymptotics on solutions to the Neumann problem for hyperbolic systems in domains with conical points. Algebra anal. 16 (2004) (In Russian.); English transl. St. Petersburg Math. J. 16 (2005), 477–506.

  10. V.G. Kondratiev: Boundary value problems for elliptic equations in domains with conical or angular points. Tr. Mosk. Mat. O.-va 16 (1967), 209–292. (In Russian.)

    Google Scholar 

  11. V.G. Kondratiev: Singularities of solutions of Dirichlet problem for second-order elliptic equations in a neighborhood of edges. Differ. Equ. 13 (1977), 2026–2032. (In Russian.)

    Google Scholar 

  12. V.A. Kozlov, V.G. Maz’ya: Spectral properties of the operator generated by elliptic boundary-value problems in a cone. Funct. Anal. Appl. 22 (1988), 114–121.

    Article  MathSciNet  MATH  Google Scholar 

  13. V.A. Kozlov, V.G. Maz’ya, J. Rossmann: Elliptic Boundary Value Problems in Domains with Point Singularities. Math. Surv. Monographs Vol. 52. American Mathematical Society, Providence, 1997.

    MATH  Google Scholar 

  14. V.A. Kozlov, V.G. Maz’ya, J. Rossmann: Spectral Problems Associated with Corner Singularities of Solutions to Elliptic Equations. Math. Surveys and Monographs Vol. 85. Americal Mathematical Society, Providence, 2001.

    MATH  Google Scholar 

  15. J.-L. Lions, F. Magenes: Non-Homogeneous Boundary Value Problems and Applications, Vol. 1. Springer, New York, 1972.

    Book  Google Scholar 

  16. J.-L. Lions, F. Magenes: Non-Homogeneous Boundary Value Problems and Applications, Vol. 2. Springer, New York, 1972.

    Book  Google Scholar 

  17. S.A. Nazarov, B.A. Plamenevskiĭ: Elliptic Problems in Domains with Piecewise-Smooth Boundary. Nauka, Moskva, 1990. (In Russian.)

    Google Scholar 

  18. V.A. Solonnikov: On the solvability of classical initial-boundary value problem for the heat equation in a dihedral angle. Zap. Nauchn. Semin. POMI 127 (1983), 7–48.

    MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Hanoi University of Education, Hanoi, Vietnam

    Nguyen Manh Hung

  2. Department of Basic Sciences, University of Transport and Communications, Hanoi, Vietnam

    Hoang Viet Long

  3. Department of Mathematics, Hanoi University of Education, Hanoi, Vietnam

    Nguyen Thi Kim Son

Authors
  1. Nguyen Manh Hung
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Hoang Viet Long
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Nguyen Thi Kim Son
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Nguyen Manh Hung.

Additional information

This research is funded by Vietnam national foundation for science and Technology development (NAFOSTED) under grant number 101.01–2011.30.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Hung, N.M., Long, H.V. & Son, N.T.K. On the asymptotics of solutions to the second initial boundary value problem for Schrödinger systems in domains with conical points. Appl Math 58, 63–91 (2013). https://doi.org/10.1007/s10492-013-0003-9

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10492-013-0003-9

Keywords

MSC 2010

Search

Navigation