Asymptotic behavior of solutions of some inverse problems for higher order parabolic equations

We consider the inverse problem of recovering an unknown term of the right-hand side of a higher-order parabolic equation. Additional information is given in the form of integral overdetermination. We establish the stabilization to zero as t tends to T of a generalized solution of the problem under consideration. In the second part of the paper we establish results on the proximity between solutions of the nonstationary and stationary inverse problems for the input data functions satisfying two possible types of assumptions, one of which permits us to treat equations with oscillating coefficients.