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This note deals with the parabolic inverse problem of determination of the leading coefficient in the heat equation with an extra condition at the terminal. After introducing a new variable, we reformulate the problem as a nonclassical parabolic equation along with the initial and boundary conditions. The existence of a solution is established by means of the Schauder fixed-point theorem.

Determination of the leading coefficient $a(x)$ in the heat equation $u_t=a(x)\Delta u$