Recovery of the time-dependent diffusion coefficient by known non-local data
S.I. Kabanikhin1,2,3, M.A. Shishlenin1,2,3
1Institute of Computational Mathematics and Mathematical Geophysics SB RAS, pr. Acad. Lavrentieva 6, Novosibirsk, 630090, Russia
2Sobolev Institute of Mathematics SB RAS, 4 Acad. Koptyug avenue, Novosibirsk, Russia, 630090
3Novosibirsk State University, Pirogova st., 2, Novosibirsk, 630090, Russia
Keywords: параболическое уравнение, коэффициентная обратная задача, численные методы, нелокальное условие, parabolic equation, time-dependent coefficient inverse problem, numerical methods, nonlocal condition
Abstract
The inverse problem of recovering the leading time-dependent coefficient by the known non-local additional information is investigated. For an approximate solution of the nonlinear inverse problems we propose the gradient method of minimizing the target functional. The comparative analysis with the method based on the linearized approximation scheme with respect to time is made. The results of the numerical calculations are presented.
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