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Abstract <p> We consider an inverse problem on finding unknown functions<InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\sigma _0\)</EquationSource> </InlineEquation> and<InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\sigma _1\)</EquationSource> </InlineEquation> that occur in the formula<InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\sigma (x,u^2)=\sigma _0+\sigma _1 u^2\)</EquationSource> </InlineEquation> for the absorption coefficient in electrodynamics equation. We obtain ana priori estimate for a solution to the direct problem and prove existence and uniqueness theoremsfor solutions to the direct and inverse problems.</p>

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An Inverse Problem for Electrodynamics Equation with Nonlinear Quadratic Absorption

  • 期刊论文

  • 发表日期：

    2025年12月22日

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  • V. G. Romanov,
  • T. V. Bugueva

摘要

Abstract

We consider an inverse problem on finding unknown functions \(\sigma _0\) and \(\sigma _1\) that occur in the formula \(\sigma (x,u^2)=\sigma _0+\sigma _1 u^2\) for the absorption coefficient in electrodynamics equation. We obtain ana priori estimate for a solution to the direct problem and prove existence and uniqueness theoremsfor solutions to the direct and inverse problems.