Inverse Problem of Determining the Absorption Coefficient in a Degenerate Parabolic Equation in the Class L ∞

Abstract

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.