Uniqueness in Linear Inverse Problems for an Abstract Differential Equation of the Second Order

We investigate linear inverse problems for a second-order abstract differential equation in a Banach space. The equation contains an independent on time inhomogeneous term. This term is unknown. At the initial moment of time the Cauchy conditions are added to the differential equation. As additional condition, an overdetermination is specified at the final moment of time. We study problems for various types of the final overdetermination. For each one a uniqueness criterion of a solution is given. These criteria are expressed in spectral terms. Simple sufficient conditions for the uniqueness and the non-uniqueness of a solution are noted. To illustrate the results, some examples are provided. The present review has been prepared as a scientific information for the conference Intelligent technologies and electronic devices in vehicle and road transport complex. This may be useful for establishing interdisciplinary connections as a theoretical basis for modeling complex systems.