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A system of Boundary-Domain Integral Equations is derived from the mixed(Dirichlet-Neumann) boundary value problem for the diffusion equation ininhomogeneous media defined on an unbounded domain. Boundary-domain integralequations are formulated in terms of parametrix-based potential type integraloperators defined on the boundary and the domain. Mapping properties ofparametrix-based potentials on weighted Sobolev spaces are analysed.Equivalence between the original boundary value problem and the system of BDIEsis shown. Uniqueness of solution of the BDIEs is proved using FredholmAlternative and compactness arguments adapted to weigthed Sobolev spaces.

communications on pure and applied analysis

Boundary-Domain Integral Equations for the Mixed Problem for the  Diffusion Equation in Inhomogeneous Media based on a New Family of  Parametrices on Unbounded Domains