Analysis of Boundary-Domain Integral Equations to the mixed BVP for a compressible stokes system with variable viscosity

Carlos Fresneda-Portillo; Sergey E. Mikhailov

doi:10.3934/cpaa.2019137

Article Contents

2019, Volume 18, Issue 6: 3059-3088. Doi: 10.3934/cpaa.2019137

This issue Previous Article Asymptotic behavior of solutions to incompressible electron inertial Hall-MHD system in $ \mathbb{R}^3 $ Next Article On a class of linearly coupled systems on

$ \mathbb{R}^N $

involving asymptotically linear terms

Analysis of Boundary-Domain Integral Equations to the mixed BVP for a compressible stokes system with variable viscosity

Carlos Fresneda-Portillo^1, , and
Sergey E. Mikhailov^2,

1.
School of Engineering, Computing and Mathematics, Wheatley Campus, Oxford Brookes University, OX33 1HX, Wheatley, UK
2.
Department of Mathematics, Brunel University London, UB8 3PH, Uxbridge, UK

^* Corresponding author
^* Corresponding author

Received: September 30, 2018

Revised: December 31, 2018

Published: May 2019

This research was supported by the grants EP/H020497/1, EP/M013545/1, and 1636273 from the EPSRC

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Abstract

The mixed boundary value problem for a compressible Stokes system of partial differential equations in a bounded domain is reduced to two different systems of segregated direct Boundary-Domain Integral Equations (BDIEs) expressed in terms of surface and volume parametrix-based potential type operators. Equivalence of the BDIE systems to the mixed BVP and invertibility of the matrix operators associated with the BDIE systems are proved in appropriate Sobolev spaces.

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Mathematics Subject Classification: Primary: 35J57, 45F15; Secondary: 45P05.

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References

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