Skip to main content
SpringerLink
Log in

Diffusion in layered media at large times

  • Published:
Theoretical and Mathematical Physics Aims and scope Submit manuscript

Abstract

The large-time asymptotic behavior of the Green's function for the one-dimensional diffusion equation is found in two cases: 1) the potential is a function with compact support; 2) the potential is a periodic function of the coordinates. In the first case, the asymptotic behavior of the Green's function can be expressed in terms of the elements of theS matrix of the corresponding Schrödinger operator for negative values of the energy on the spectral plane. In the second case, the asymptotic behavior can be expressed in terms of Floquet-Bloch functions of the corresponding Hille operator at negative values of the energy on the spectral plane. The results are used to study diffusion in layered media at large times. The case of external force is also considered. In the periodic case, the Seeley coefficients are found.

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. E. L. Korotyaev, in:Proc. of 14th International School on the Theory of Linear Operators in Function Spaces [in Russian], Nizhne Novgorod University, Nizhne Novgorod (1991).

    Google Scholar 

  2. L. D. Faddeev,Tr. Mosk. Inst. Akad. Nauk,73, 314 (1964).

    Google Scholar 

  3. N. E. Firsova,Mat. Sb.,130(172), 349 (1986).

    Google Scholar 

  4. M. V. Fedoryuk,The Method of Steepest Descent [in Russian], Nauka, Moscow (1977).

    Google Scholar 

  5. N. E. Firsova,Zap. Nauchn. Semin. LOMI,51, 183 (1975).

    Google Scholar 

  6. V. A. Marchenko and I. V. Ostrovskii,Mat. Sb.,97(139), 540 (1975).

    Google Scholar 

  7. R. T. Seeley,Proc. Symp. in Pure Math.,10, 288 (1967).

    Google Scholar 

  8. B. M. Levitan,Inverse Sturm-Liouville Problems [in Russian], Nauka, Moscow (1984).

    Google Scholar 

  9. E. C. Titchmarsh,Eigenfunction Expansions Associated with Second-Order Differential Equations, Vol. II, Clarendon Press, Oxford (1958).

    Google Scholar 

  10. N. E. Firsova,Mat. Zametki,36, 711 (1984).

    Google Scholar 

  11. E. L. Korotyaev,Zap. Nauchn. Semin. LOMI,195, 48 (1991).

    Google Scholar 

  12. A. R. Its and V. B. Matveev,Teor. Mat. Fiz.,23, 51 (1975).

    Google Scholar 

  13. A. Hurwitz (and R. Courant),Vorlesungen über allgemeine Funktionentheorie und elliptische Funktionen, Berlin (1964).

Download references

Authors
  1. E. L. Korotyaev
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. N. E. Firsova
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Institute of Problems of Mechanical Engineering, Russian Academy of Sciences. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 98, No. 1, pp. 106–148, January, 1994.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Korotyaev, E.L., Firsova, N.E. Diffusion in layered media at large times. Theor Math Phys 98, 72–99 (1994). https://doi.org/10.1007/BF01015126

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01015126

Keywords

Search

Navigation