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Abstract <p>Kelvin–Voigt equations for inhomogeneous fluids with a singular right side are studied. A&#xa0;singular term that approximates the Dirac delta function on an initially infinitely thin layer is introduced into the right side of a mass balance equation. This singular term is similar to the relaxation term used to describe nonequilibrium processes in hydrodynamics. In an extreme case, when a small parameter, namely, the characteristic size of the initial layer, tends to zero, the density and velocity at the initial time change abruptly.</p>

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Kelvin–Voigt Equations with a Discontinuous Density Profile

  • 期刊论文

  • 发表日期：

    2025年2月1日

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  • S. N. Antontsev,
  • I. V. Kuznetsov

摘要

Abstract

Kelvin–Voigt equations for inhomogeneous fluids with a singular right side are studied. A singular term that approximates the Dirac delta function on an initially infinitely thin layer is introduced into the right side of a mass balance equation. This singular term is similar to the relaxation term used to describe nonequilibrium processes in hydrodynamics. In an extreme case, when a small parameter, namely, the characteristic size of the initial layer, tends to zero, the density and velocity at the initial time change abruptly.