SOME IDENTIFICATION PROBLEMS FOR INTEGRO-DIFFERENTIAL OPERATOR EQUATIONS

Abstract

We consider, in a Hilbert space H, the convolution integro-differential equation u''(t)-h*Au(t) = f(t), 0 leq t leq T, h* v(t) =int_0^t h(t-s)v(s) ds, where A is a linear closed densely defined (possibly selfadjoint and/or positive definite) operator in H. Under suitable assumptions on the data we solve the inverse problem consisting of finding the kernel h from the extra data (measured data) of the type g(t):= (u(t),b), where b is some eigenvector of A*. An inverse problem for the first-order equation u'(t)-l*Au(t) = f(t), is also studied when A enjoys the same properties as in the previous case.