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<p>The Dirichlet boundary value problem (BVP) for a compressible Stokes system of partial differential equations (PDEs) with variable viscosity is considered in a bounded three-dimensional domain. Using an appropriate parametrix (Levi function), the problem is reduced to the united boundary-domain integro-differential equation (BDIDE) or to a domain integral equation supplemented by the original boundary condition, thus constituting a boundary-domain integro-differential problem (BDIDP). The Dirichlet data are derived from spaces <b>H</b> <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\( ^{1/2}(\partial \Omega )\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mmultiscripts> <mrow /> <mrow /> <mrow> <mn>1</mn> <mo stretchy="false">/</mo> <mn>2</mn> </mrow> </mmultiscripts> <mrow> <mo stretchy="false">(</mo> <mi>∂</mi> <mi mathvariant="normal">Ω</mi> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation>. Solvability, solution uniqueness, and equivalence of the BDIDEs/BDIDP to the original BVP as well as invertibility of the associated operators are analyzed in appropriate Sobolev (Bessel potential) spaces.</p>

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ANALYSIS OF UNITED BOUNDARY-DOMAIN INTEGRAL AND INTEGRO-DIFFERENTIAL EQUATIONS TO THE DIRICHLET PROBLEM FOR A COMPRESSIBLE STOKES SYSTEM WITH VARIABLE VISCOSITY

  • 期刊论文

  • 发表日期：

    2025年6月1日

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  • Tsegaye G. Ayele,
  • Goitom W. Hagos

摘要

The Dirichlet boundary value problem (BVP) for a compressible Stokes system of partial differential equations (PDEs) with variable viscosity is considered in a bounded three-dimensional domain. Using an appropriate parametrix (Levi function), the problem is reduced to the united boundary-domain integro-differential equation (BDIDE) or to a domain integral equation supplemented by the original boundary condition, thus constituting a boundary-domain integro-differential problem (BDIDP). The Dirichlet data are derived from spaces H \( ^{1/2}(\partial \Omega )\) 1 / 2 ( ∂ Ω ) . Solvability, solution uniqueness, and equivalence of the BDIDEs/BDIDP to the original BVP as well as invertibility of the associated operators are analyzed in appropriate Sobolev (Bessel potential) spaces.