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.
Cite this article
Jaan Janno, Alfredo Lorenzi, Recovering Degenerate Kernels in Hyperbolic Integro-Differential Equations. Z. Anal. Anwend. 21 (2002), no. 2, pp. 399–430DOI 10.4171/ZAA/1085