On the existence and uniqueness of solution of boundary‐domain integral equations for the Dirichlet problem for the nonhomogeneous heat transfer equation defined on a 2D unbounded domain

Abstract

A system of boundary-domain integral equations (BDIEs) is obtained from the Dirichlet problem for the diffusion equation in nonhomogeneous media defined on an exterior two-dimensional domain. We use a parametrix different from the one employed in Dufera and Mikhailov (2019). The system of BDIEs is formulated in terms of parametrix-based surface and volume potentials whose mapping properties are analyzed 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.