Inverse problem of determining the absorption coefficient in a multidimensional nonuniformly parabolic equation

The unique solvability of the inverse problem of determining the $x$-dependent lower coefficient in a nonuniformly parabolic equation with many independent variables in a bounded domain is proved. As an additional condition, the integral observation condition is specified. In addition, we obtain estimates of the solution with constants explicitly written in terms of the input data of the inverse problem. An example of inverse problems for which the results proved in the paper are applicable is given.