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On the Existence and Uniqueness of Solution of Boundary-Domain Integral Equations for the Dirichlet Problem for the Non-Homogeneous Heat Transfer Equation defined on a 2D Unbounded Domain
  • Zenebe Woldemicheal,
  • C. Fresneda-PortilloOrcid
Zenebe Woldemicheal
Addis Ababa University
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C. Fresneda-Portillo
Orcid
Oxford Brookes Univ
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Peer review status:UNDER REVIEW

27 Mar 2020Submitted to Mathematical Methods in the Applied Sciences
03 Apr 2020Assigned to Editor
03 Apr 2020Submission Checks Completed
10 Apr 2020Review(s) Completed, Editorial Evaluation Pending
10 Apr 2020Reviewer(s) Assigned

Abstract

A system of boundary-domain integral equations (BDIEs) is obtained from the Dirichlet problem for the diffusion equation in non-homogeneous media defined on an exterior two-dimensional domain. We use a parametrix different from the one employed by in \cite{dufera}. The system of BDIEs is formulated in terms of parametrix-based surface and volume potentials whose mapping properties are analysed in weighted Sobolev spaces. The system of BDIEs is shown to be equivalent to the original boundary value problem and uniquely solvable in appropriate weighted Sobolev spaces suitable for unbounded domains.