Durdiev, Durdimurod Kalandarovich; Totieva, Zhanna Dmitrievna The problem of determining the one-dimensional kernel of viscoelasticity equation with a source of explosive type. (English) Zbl 1437.35465 J. Inverse Ill-Posed Probl. 28, No. 1, 43-52 (2020). Summary: The integro-differential system of viscoelasticity equations with a source of explosive type is considered. It is assumed that the coefficients of the equations depend only on one spatial variable. The problem of determining the kernel included in the integral terms of the equations is studied. The solution of the problem is reduced to one inverse problem for scalar hyperbolic equations. This inverse problem is replaced by an equivalent system of integral equations for unknown functions. The principle of constricted mapping in the space of continuous functions with weighted norms to the latter is applied. The theorem of global unique solvability is proved and the stability estimate of solution to the inverse problem is obtained. Cited in 8 Documents MSC: 35L53 Initial-boundary value problems for second-order hyperbolic systems 35R30 Inverse problems for PDEs 35Q74 PDEs in connection with mechanics of deformable solids Keywords:delta function; Lame’s coefficients; kernel reconstruction PDFBibTeX XMLCite \textit{D. K. Durdiev} and \textit{Z. D. Totieva}, J. Inverse Ill-Posed Probl. 28, No. 1, 43--52 (2020; Zbl 1437.35465) Full Text: DOI References: [1] A. L. Bukhgeim, N. I. Kalinina and V. B. Kardakov, Two methods for the inverse problem of memory reconstruction (in Russian), Sibirsk. Mat. Zh. 41 (2000), no. 4, 767-776; translation in Sib. Math. J. 41 (2000), no. 4, 634-642. · Zbl 0958.35148 [2] D. K. Durdiev, An inverse problem for determining two coefficients in an integrodifferential wave equation, Sib. Zh. Ind. Mat. 12 (2009), no. 3, 28-40. · Zbl 1240.35575 [3] D. K. 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