Geodesic
Diffusion in layered media at large time
Teoretičeskaâ i matematičeskaâ fizika, Tome 98 (1994) no. 1, pp. 106-148 Cet article a éte moissonné depuis la source Math-Net.Ru

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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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E. L. Korotyaev; N. E. Firsova. Diffusion in layered media at large time. Teoretičeskaâ i matematičeskaâ fizika, Tome 98 (1994) no. 1, pp. 106-148. http://geodesic.mathdoc.fr/item/TMF_1994_98_1_a9/

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