Under study is the inverse problem of determining the two-dimensional kernel for a system of viscoelasticity equations in a medium with slightly horizontal homogeneity in a half-space. The direct initial-boundary value problem for the displacement function contains zero initial data and the Neumann condition of a special form. The field of displacements of medium points is given for x 3 − 0 as additional information. We assume that the kernel decomposes into an asymptotic series, construct some method for determining the kernel with accuracy of O ( ε 2 ) where ε is a small parameter, and prove the theorems of global unique solvability and stability of the solution to the inverse problem.

中文翻译：

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确定具有轻微水平均匀性的介质中粘弹性方程的核

正在研究的是确定在半空间中具有轻微水平均匀性的介质中粘弹性方程系统的二维核的逆问题。位移函数的直接初边值问题包含零初始数据和特殊形式的诺依曼条件。x 3 − 0 的中点位移场作为附加信息给出。我们假设核分解为渐近级数，构造一些确定核的方法，其精度为 O ( ε 2 )，其中 ε 是一个小参数，并证明了逆问题解的全局唯一可解性和稳定性定理.