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Abstract <p> The inverse problem of determining two unknown functions<InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\sigma _0(x)\)</EquationSource> </InlineEquation> and<InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\sigma _1(x)\)</EquationSource> </InlineEquation> included in the absorption coefficient<InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\sigma (x,u)=\sigma _0(x)+\sigma _1(x)u\)</EquationSource> </InlineEquation> in the equation of electrodynamics is considered. An a priori estimate of thesolution to the direct problem is obtained, and the existence and uniqueness theorems of solutionsto the direct and inverse problems are proved.</p>

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An Inverse Problem for the Equation of Electrodynamics with Nonlinear Absorption

  • 期刊论文

  • 发表日期：

    2025年6月1日

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  • V. G. Romanov,
  • T. V. Bugueva

摘要

Abstract

The inverse problem of determining two unknown functions \(\sigma _0(x)\) and \(\sigma _1(x)\) included in the absorption coefficient \(\sigma (x,u)=\sigma _0(x)+\sigma _1(x)u\) in the equation of electrodynamics is considered. An a priori estimate of thesolution to the direct problem is obtained, and the existence and uniqueness theorems of solutionsto the direct and inverse problems are proved.