Asymptotic behaviour of the solutions of inverse problems for parabolic equations with irregular coefficients

The problem of asymptotic proximity as $t\to\infty$ of the solutions of the inverse problem for a parabolic equation with an unknown right-hand side and the solution of the limiting stationary inverse problem in a bounded domain is studied. The overdetermination conditions are given in integral form. The conditions on the proximity of the coefficients of the stationary and the non-stationary problems are formulated in a certain very weak sense, which allows, in particular, oscillations of the coefficients.