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United Boundary-Domain Integro-Differential and Integral Equations to the Mixed BVP for a Compressible Stokes System with Variable Viscosity

Author

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  • Goitom W. Hagos
  • Tsegaye G. Ayele
  • Francisco J. Garcia-Pacheco

Abstract

The mixed BVP for a compressible Stokes system of PDEs with variable viscosity is considered in a bounded domain of three dimensions. Based on a specially constructed parametrix (Levi function), the problem is reduced to the united boundary-domain integro-differential or integral equations (BDIDEs or BDIEs). The BDIDEs are to be supplemented by the original boundary conditions, thus constituting boundary-domain integro-differential problems (BDIDPs). The BDIDPs/BDIEs contain integral operators defined on the domain under consideration as well as potential-type operators defined on open submanifolds of the boundary and acting on the trace and/or traction of the unknown solution or on an auxiliary function. Solvability, solution uniqueness, equivalence of the BDIDPs/BDIEs to the original BVP, and invertibility of the associated operators are investigated in appropriate Sobolev spaces.

Suggested Citation

  • Goitom W. Hagos & Tsegaye G. Ayele & Francisco J. Garcia-Pacheco, 2024. "United Boundary-Domain Integro-Differential and Integral Equations to the Mixed BVP for a Compressible Stokes System with Variable Viscosity," Journal of Mathematics, Hindawi, vol. 2024, pages 1-19, December.
    • Handle: RePEc:hin:jjmath:8101059
    DOI: 10.1155/2024/8101059
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