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A new approximate mathematical model for global convergence for a coefficient inverse problem with backscattering data. (English) Zbl 1279.35094

Summary: An approximately globally convergent numerical method for a 3d coefficient inverse problem for a hyperbolic equation with backscattering data is presented. A new approximate mathematical model is presented as well. An approximation is used only on the first iteration and amounts to the truncation of a certain asymptotic series. A significantly new element of the convergence analysis is that the so-called “tail functions” are estimated. Numerical results in 2d and 3d cases are discussed, including the one for a quite heterogeneous medium.

MSC:

35R25 Ill-posed problems for PDEs
35R30 Inverse problems for PDEs
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