An inverse problem for a pseudoparabolic integro-differential operator equation (Q1921814)

The authors consider some inverse problem for a pseudoparabolic differential operator equation. They prove existence and uniqueness theorems and obtain a stability estimate. Similar questions for parabolic and hyperbolic integro-differential equations were studied in [\textit{A. Lorenzi} and \textit{E. Sinestrari}, Nonlinear Anal., Theor. Methods Appl. 12, No. 12, 1317-1335 (1988; Zbl 0673.45010), \textit{M. Grasselli}, \textit{S. I. Kabanikhin} and \textit{A. Lorenzi}, Sib. Mat. Zh. 33, No. 3, 58-68 (1992; Zbl 0787.46006)]. However, these methods are not applicable to the parabolic equation under consideration. The authors consider the problem with an extra condition of special form which allows them to reduce the inverse problem in question to a nonlinear Volterra operator equation of the second kind.