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This work focuses on solving inverse problem for a wave equation with a non-local potential. The novelty of the work is in the statement of the forward and inverse non-stationary problems for a wave equation with a non-local potential and the method of solving them. The method of solving the forward and inverse non-stationary problems is based on the close use of sufficiently developed approaches for the stationary Shr odinger equation. From the mathematical physics point of view, the practical value of this work is in the development of methods for determining the discrete spectrum of stationary problem for the Shr odinger equation with a non-local potential using some data from the inverse non-stationary problem for a wave equation with a non-local potential. From the passive seismic point of view, it means the reconstruction of the environment structure based on the measurements, since determining the eigenvalues is equivalent to determining eigenfrequencies of the environment. The book would be useful for researchers and graduate students in the areas of physical mathematics, applied mathematics and geophysics.

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Dr. Durmagambetov received his Ph.D in Physical Mathematics from Almaty, Kazakhstan in 1987. His research interests include nonlinear differential equations, variational methods, inverse problems, mathematical and computational modeling. Dr. Durmagambetov has solved one of Millennium Prize problems - Navier-Stokes existence and smoothness problem.

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