Inverse problem for integro-differential Kelvin–Voigt equations

Abstract

Abstract In this paper, the existence and uniqueness of a strong solution of the inverse problem of determining a coefficient of right-hand side of the integro-differential Kelvin–Voigt equation are investigated. The unknown coefficient that we search defends on space variables. Additional information on a solution of the inverse problem is given here as an integral overdetermination condition. The original inverse problem is reduced to study an equivalent inverse problem with homogeneous initial condition. Then the equivalences of the last inverse problem to an operator equation of second kind is proved. We establish the sufficient conditions for the unique solvability of the operator equation of second kind.