The Inverse Problem of Simultaneous Determination of the Two Time-Dependent Lower Coefficients in a Nondivergent Parabolic Equation in the Plane

We prove existence and uniqueness theorems for the solution of the inverse problem of simultaneous determination of the $t$-dependent coefficients of $u$ and $u_x$ in a nondivergent parabolic equation with two independent variables from integral observation of $x$. Estimates of the maxima of the moduli of these coefficients with constants explicitly expressed in terms of the input data of the problem are given. An example of an inverse problem to which the proved theorems apply is presented.