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Abstract <p> A thermoelectric <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\((3+1)\)</EquationSource> </InlineEquation>-dimensional model of heating a dielectric in an electric field is considered which takes into account the Kerr nonlinear dependence of permittivity on the magnitude of field strength. For the corresponding Cauchy problem, the existence of a noncontinuable classical solution is proved and a result concerning the blow-up of a solution is obtained. </p>

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Blow-up of Solutions of the Cauchy Problem for the Doubly Nonlinear Equation of a Thermoelectric Model

  • 期刊论文

  • 发表日期：

    2025年8月1日

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  • M. V. Avtushenko,
  • M. O. Korpusov,
  • A. K. Matveeva

摘要

Abstract

A thermoelectric \((3+1)\) -dimensional model of heating a dielectric in an electric field is considered which takes into account the Kerr nonlinear dependence of permittivity on the magnitude of field strength. For the corresponding Cauchy problem, the existence of a noncontinuable classical solution is proved and a result concerning the blow-up of a solution is obtained.