Inverse problem of determining the absorption coefficient in a degenerate parabolic equation in the class $L_\infty$

Existence and uniqueness theorems for solutions of inverse problems of determining the time-dependent absorption coefficient in a degenerate parabolic equation with two independent variables are proved. An integral observation condition is additionally imposed. The unknown absorption coefficient is sought in the class of bounded functions on $[0,T]$. Examples of the inverse problems are given for which the conditions of the theorems proved in the work are satisfied.