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The problem of determining the one-dimensional kernel of viscoelasticity equation with a source of explosive type. (English) Zbl 1437.35465
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.

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
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