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TMF, 1994, Volume 98, Number 1, Pages 106–148 (Mi tmf1405)  

Diffusion in layered media at large time

E. L. Korotyaev, N. E. Firsova

Institute of Problems of Mechanical Engineering, Russian Academy of Sciences

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 the $S$ 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.

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English version:
Theoretical and Mathematical Physics, 1994, 98:1, 72–99

Bibliographic databases:

Received: 02.10.1991
Revised: 12.04.1993

Citation: E. L. Korotyaev, N. E. Firsova, “Diffusion in layered media at large time”, TMF, 98:1 (1994), 106–148; Theoret. and Math. Phys., 98:1 (1994), 72–99

Citation in format AMSBIB
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\by E.~L.~Korotyaev, N.~E.~Firsova
\paper Diffusion in layered media at large time
\jour TMF
\yr 1994
\vol 98
\issue 1
\pages 106--148
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\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1291371}
\zmath{https://zbmath.org/?q=an:0818.34050}
\transl
\jour Theoret. and Math. Phys.
\yr 1994
\vol 98
\issue 1
\pages 72--99
\crossref{https://doi.org/10.1007/BF01015126}
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  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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