The problem of recovering a degenerate operator kernel in a hyperbolic integrodifferential 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.
|Titolo:||Recovering degenerate kernels in hyperbolic integro-differential equations|
LORENZI, ALFREDO (Ultimo)
|Parole Chiave:||Hyperbolic integro-differential equations; Identification problems; Second-order integro-differential operator equations; Space- and time-dependent degenerate relaxation kernels|
|Settore Scientifico Disciplinare:||Settore MAT/05 - Analisi Matematica|
|Data di pubblicazione:||2002|
|Digital Object Identifier (DOI):||10.4171/ZAA/1085|
|Appare nelle tipologie:||01 - Articolo su periodico|