Abstract
In this paper, we formulate a global theorem of uniqueness of the solution of the inverse problem fro the recostruction of a special-kind source in heat equation. As a overdetermination we take comact-support trace of the solution on an internal segment inside the domain at the final moment of time. We assume the symmetry of the domain along the coordinate axis and the validity of some restrictions on the signs of a given term in the source and its derivatives. No restrictions on the size of the domain or on the absolute value of the given functions assumed. We prove corresponding facts for the solution of the direct problem. These are maximum principle and belonging of the solution to the peculiar class of functions.
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