The problem of determining the multidimensional kernel of viscoelasticity equation. (Russian. English summary) Zbl 1474.45100

Summary: The integro-differential system of viscoelasticity equations is considered. The direct problem of determining of the displacements vector from the initial-boundary problem for this system is formulated. It is assumed that the kernel in the integral part depends on both the time and the space variable \(x_2\). For its determination an additional condition relative to the first component of the displacements vector with \(x_3=0\) is posed. The inverse problem is replaced by the equivalent system of integral equations. The study is based on the method of scales of Banach spaces of analytic functions. The theorem on local unique solvability of the inverse problem is proved in the class of functions analytic on the variable \(x_2\) and continuous on \(t\).


45Q05 Inverse problems for integral equations
45K05 Integro-partial differential equations
74D05 Linear constitutive equations for materials with memory
Full Text: MNR


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