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Zeitschrift für Analysis und ihre Anwendungen

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Volume 21, Issue 2, 2002, pp. 399–430
DOI: 10.4171/ZAA/1085

Published online: 2002-06-30

Recovering Degenerate Kernels in Hyperbolic Integro-Differential Equations

Jaan Janno[1] and Alfredo Lorenzi[2]

(1) Tallin Technical University, Estonia
(2) Università degli Studi di Milano, Italy

The problem of recovering a degenerate operator kernel in a hyperbolic integro-differential operator equation is studied. Existence, uniqueness and stability for the solution are proved. A conditional convergence of a sequence of solutions corresponding to degenerate kernels to a solution corresponding to a non-degenerate kernel is shown. Such results are applied to determine space- and time-dependent relaxation kernels in a multi-dimensional viscoelastic wave equation with given boundary observations of traction type on the assumption that the kernels to be determined are representable as a finite or infinite sum of products of known space-dependent and unknown time-dependent functions.

Keywords: Identification problems, hyperbolic integro-differential equations, secondorder integro-differential operator equations, space- and time-dependent degenerate relaxation kernels

Janno Jaan, Lorenzi Alfredo: Recovering Degenerate Kernels in Hyperbolic Integro-Differential Equations. Z. Anal. Anwend. 21 (2002), 399-430. doi: 10.4171/ZAA/1085