### Tabarintseva E.

## Approximate solving of an inverse problem for a parabolic equation with nonlocal data

We consider the problem of controlling the temperature distribution in the rod, the lateral surface of which is thermally insulated, zero temperature is maintained at the left end, and the change in the amount of heat in the rod is zero. The control is carried out by the unknown initial temperature distribution. The task is ill-posed in the considered functional spaces, the operator of the problem is non-self-adjoint. An approximate solution is constructed using a regularization method, which consists in replacing the unstable initial problem by a stable problem with a small parameter. An exact in order error estimate is obtained for the constructed approximate solution.

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