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Abstract <p> A new boundary value problem for the stationary heat and mass transfer equations withvariable coefficients is considered. It is assumed that the leading viscosity, thermal conductivity,and diffusion coefficients, as well as the buoyancy force, occurring in the equations depend on thetemperature and the concentration of the substance dissolved in the base medium.A mathematical technique based on a variational approach is developed to study this boundaryvalue problem. This technique is used to prove the global existence of a weak solution of theboundary value problem and establish sufficient conditions on the problem data ensuring the localuniqueness of a weak solution under the additional condition that the temperature andconcentration are smooth.</p>

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Solvability of a Boundary Value Problem for the Stationary Heat and Mass Transfer Equations with Variable Coefficients

  • 期刊论文

  • 发表日期：

    2025年12月1日

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  • G. V. Alekseev,
  • O. V. Soboleva

摘要

Abstract

A new boundary value problem for the stationary heat and mass transfer equations withvariable coefficients is considered. It is assumed that the leading viscosity, thermal conductivity,and diffusion coefficients, as well as the buoyancy force, occurring in the equations depend on thetemperature and the concentration of the substance dissolved in the base medium.A mathematical technique based on a variational approach is developed to study this boundaryvalue problem. This technique is used to prove the global existence of a weak solution of theboundary value problem and establish sufficient conditions on the problem data ensuring the localuniqueness of a weak solution under the additional condition that the temperature andconcentration are smooth.