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Abstract <p> The two-dimensional inverse problem of determining the kernel of an elasticity equation ofmemory type is studied. It is assumed that the coefficients of the equations depend on only onespatial variable. Applying the linearization principle, the inverse problem is reduced to anequivalent linear system of integral equations. The generalized principle of compressed maps isapplied to the latter in the space of continuous functions. The theorem of unique solvability isproved and an estimate of the stability of the solution to the inverse problem is obtained.</p>

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Two-Dimensional Inverse Problem for a Viscoelasticity Equation in a Vertically Inhomogeneous Medium

  • 期刊论文

  • 发表日期：

    2025年11月2日

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  • Zh. D. Totieva

摘要

Abstract

The two-dimensional inverse problem of determining the kernel of an elasticity equation ofmemory type is studied. It is assumed that the coefficients of the equations depend on only onespatial variable. Applying the linearization principle, the inverse problem is reduced to anequivalent linear system of integral equations. The generalized principle of compressed maps isapplied to the latter in the space of continuous functions. The theorem of unique solvability isproved and an estimate of the stability of the solution to the inverse problem is obtained.