# American Institute of Mathematical Sciences

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November  2019, 18(6): 3059-3088. doi: 10.3934/cpaa.2019137

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

 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

Received  October 2018 Revised  January 2019 Published  May 2019

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

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.

Citation: Carlos Fresneda-Portillo, Sergey E. Mikhailov. Analysis of Boundary-Domain Integral Equations to the mixed BVP for a compressible stokes system with variable viscosity. Communications on Pure & Applied Analysis, 2019, 18 (6) : 3059-3088. doi: 10.3934/cpaa.2019137
##### References:

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