Inverse Problem with Integral Overdetermination for System of Equations of Kelvin-Voight Fluids

Abstract

In the paper we consider an inverse problem for the three-dimensional nonlinear pseudoparabolic equations describing the Kelvin-Voight motion. The inverse problem consists of finding a velocity field and pressure which is gradient and also a right-hand said of the equation. Additional condition about the solution to the inverse problem is given in the form of integral overdetermination condition. The existence and uniqueness of weak generalized solution of this inverse problem in the sobelev space is proved.