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

摘要

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 documentclass12pt{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$0,T$$end{document} . Examples of the inverse problems are given for which the conditions of the theorems proved in the work are satisfied.