New analogue of M.G. Krein equation for 1D acoustic inverse problem with the arbitrary source function
New analogue of M.G. Krein equation for 1D acoustic inverse problem with the arbitrary source function
(Russian, English abstract)
Siberian Electronic Mathematical Reports, 22, 2, pp. 1741-1749 (2025)
Abstract:
The article considers the 1D coefficient inverse problem for the acoustic equation. New version of the I.M. Gelfand - B.M. Levitan - M.G. Krein approach, applicable for the general time form of the sounding wave, is proposed. The new set of linear integral equations, equivalent to the inverse problem, is obtained.
Keywords: coefficient inverse problems, ill-posed problems, direct methods, integral equations.