Identification problems for nonclassical integro-differential parabolic equations

In this paper we identify a convolution kernel k — i.e. we prove existence and uniqueness of k — in a first-order singular integrodifferential operator equation of Volterra type in two overdetermined problems in the framework of Hilbert spaces. We stress that in the first problem, by virtue of specific nonlocal time conditions, the kernel can be recovered globally in time, while in the latter only locally in time because of conditions that are of time-periodic type.