GLOBAL SOLVABILITY OF INVERSE PROBLEM FOR LINEAR KELVIN-VOIGT EQUATIONS WITH MEMORY

In this paper, the inverse problem for a linear system of Kelvin-Voigt equations with memory describing dynamics viscoelastic incompressible non-newtonian fluid is considered. under consideration, along solution (velocity and pressure) equation, it also required to find unknown (intensity external force) on right side, which depends only time variable. Definitions weak strong solutions are given. Weak set problems satisfy boundary condition sliding at boundary. The gives mathematical physical character study memory. applicability Faedo-Galerkin method type analyzed. With help method, global theorem existence presented proved in generalized sense. To prove "as whole"in time, associated obtaining priori estimates, constants depend data magnitude interval. And uniqueness considered obtained proved.