In addition to studying the correctness of problems in mathematical physics, that is, the existence, uniqueness, and stability of solutions, it is also important to study the qualitative
properties of these solutions. In general, proving the global existence and uniqueness of solutions to
direct and inverse problems for nonlinear equations and systems of equations in mathematical
physics and hydrodynamics is not easy, since there are no universal methods for solving nonlinear problems. However, studying some qualitative properties of solutions, such as the blowup of a solution in finite time, localization of solutions, or a large time behaviour of solutions, etc., can
provide an idea of the nature of the general change in estimates or solutions. In this paper, we
consider the inverse problem of determining the coefficient of the right-hand side as a function of
time for a system of linear Kelvin-Voigt (Oskolkov) equations describing the flow of an incompressible viscoelastic fluid. The results on the existence and uniqueness of strong and weak
solutions to corresponding problem has been studied. In this article, based on the results of the mentioned work, an asymptotic property of the generalized weak solution of the indicated inverse problem is shown, namely, exponential decay.