Eigenvalue asymptotics of layered media and their applications to the inverse problem
Athanassoulis, Gerasimos A. Papanicolaou, Vassilis G
Athanassoulis, Gerasimos A.
Papanicolaou, Vassilis G
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1997
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Article
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Eigenvalue asymptotics,Layered medium,Piecewise smooth potential,Reconstruction of jumps
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Athanassoulis, G., & Papanicolaou, V. (1997). Eigenvalue Asymptotics of Layered Media and Their Applications to the Inverse Problem. SIAM Journal on Applied Mathematics, 57(2), 453-471.
Abstract
We compute the asymptotics of the eigenvalues of the classical Sturm-Liouville problem with a piecewise smooth coefficient q. This means that q and/or its derivatives can have jump discontinuities. The boundary conditions are arbitrary. Our results extend the classical work of H. Hochstadt (see [Comm. Pure Appl. Math., 14 (1961), pp. 749-764]) and some related formulas discovered by G. Borg (see [Acta Math., 78 (1946), pp. 1-96]). Then, we apply our results to the inverse problem of determining the interfaces in a layered medium from acoustic data, since the index of refraction of such a medium can be considered piecewise smooth.
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Society for Industrial and Applied Mathematics Publications
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SIAM Journal on Applied Mathematics
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0036-1399