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Boundary-Domain Integral Equation Systems to the Mixed BVP for Compressible Stokes Equations with Variable Viscosity in 2D
  • Mulugeta A Dagnaw,
  • Tsegaye G Ayele
Mulugeta A Dagnaw
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Tsegaye G Ayele
Addis Ababa University
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Abstract

In this paper, the Boundary-Domain Integral Equations (BDIEs) for the mixed boundary value problem(BVP) for a compressible Stokes system of partial differential equation (PDE) with variable coefficient in 2D is considered . An appropriate parametrix is used to reduce this BVP to the BDIEs. Although the theory of BDIEs in 3D is well developed, the BDIEs in 2D need a special consideration due to their different equivalence properties. As a result, we need to set conditions on the domain or on the spaces to ensure the invertibility of corresponding parametrix-based integral layer potentials and hence the unique solvability of BDIEs. The properties of corresponding potential operators are investigated. Equivalence of the BDIE systems to the mixed BVP and invertibility of the matrix operators associated with the BDIE systems in appropriate Sobolev spaces are proved.

Peer review status:ACCEPTED

30 Jan 2020Submitted to Mathematical Methods in the Applied Sciences
01 Feb 2020Submission Checks Completed
01 Feb 2020Assigned to Editor
05 Feb 2020Reviewer(s) Assigned
19 Nov 2020Review(s) Completed, Editorial Evaluation Pending
20 Nov 2020Editorial Decision: Revise Minor
23 Nov 20201st Revision Received
23 Nov 2020Submission Checks Completed
23 Nov 2020Assigned to Editor
23 Nov 2020Reviewer(s) Assigned
23 Nov 2020Review(s) Completed, Editorial Evaluation Pending
24 Dec 2020Editorial Decision: Accept