Localized Boundary-Domain Integro-Differential Equations Approach for Stationary Heat Transfer Equation

Localized boundary-domain integro-differential equations (LBDIDE) systems associated with the Dirichlet and Robin boundary value problems (BVP) for the stationary heat transfer partial differential equation (PDE) with a variable coefficient are obtained and analysed. Localization is performed by a non-smooth parametrix represented as the product of a global parametrix and the characteristic function of a ball centered at a reference point. The equivalence of the LBDIDE systems to the original variable-coefficient BVPs and unique solvability of the LBDIDE systems in appropriate Sobolev spaces are the main results of the present paper.