Identification of the memory kernel in the strongly damped wave equation by a flux condition

We study an abstract inverse problem of reconstruction of the solution of a semilinear mixedintegrodifferential parabolic problem, together with a convolution kernel. The supplementaryinformation required to solve the problem also involves a convolution termwith the same unknown kernel. Theabstract results are applicable to the identification of a memory kernel in a strongly damped waveequation using a flux condition.