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

Abstract

A system of segregated 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 (Dufera, 2019). 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 infinite domains.

arXiv comment17 pages

References in corpus (4)

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• Analysis of a Boundary-Domain Integral Equation System for the Mixed Interior Diffusion BVP with Variable Coefficient Based on a New Family of Parametrices
• Singular Localised Boundary-Domain Integral Equations of Acoustic Scattering by Inhomogeneous Anisotropic Obstacle
• On the Existence of Solution of the Boundary-Domain Integral Equation System derived from the 2D Dirichlet Problem for the Diffusion Equation with Variable Coefficient