Abstract
The iterative asymptotic method for solving inverse problems for partial differential equations was developed for the case of slowly varying coefficients. The method constructs a sequence that is proved to converge asymptotically to the solution of the inverse problem. We indicate cases in which this sequence uniformly converges to the solution of the inverse problem.
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References
Barashkov, A.S. and Dmitriev, V.I., On an Inverse Problem of Deep Magnetotelluric Probing, Dokl. Akad. Nauk SSSR, 1987, vol. 295, no. 1, pp. 83–86.
Barashkov, A.S., Asymptotic Representations of the Solution of an Inverse Problem for the Helmholtz Equation, Zh. Vychisl. Mat. Mat. Fiz., 1988, vol. 28, no. 12, pp. 1823–1831.
Barashkov, A.S., Small Parameter Method in Multidimensional Inverse Problems, Utrecht, 1998.
Berdichevskii, M.N. and Dmitriev, V.N., Modeli i metody magnitotelluriki (Models and Methods of Magnetotellurics), Moscow, 2009.
Bakhvalov, N.S., Chislennye metody (Numerical Methods), Moscow: Nauka, 1973.
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Original Russian Text © A.S. Barashkov, A.A. Nebera, 2015, published in Differentsial’nye Uravneniya, 2015, Vol. 51, No. 4, pp. 548–552.
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Barashkov, A.S., Nebera, A.A. Cases of uniform convergence of the iterative asymptotic method for solving multidimensional inverse problems. Diff Equat 51, 558–562 (2015). https://doi.org/10.1134/S0012266115040126
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DOI: https://doi.org/10.1134/S0012266115040126