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Fundamental solutions for steady-state heat transfer in an exponentially graded anisotropic material. (English) Zbl 1063.35012
Summary: Heat conduction in an anisotropic inhomogeneous medium is considered. The conductivities vary exponentially in one fixed but arbitrary direction. The Green’s function corresponding to a point source is constructed. Two methods are used, one using Fourier transforms and one involving certain changes of variables in the governing partial differential equation. Solutions in two and three dimensions are derived. They can be used as a basic ingredient in the formulation of boundary integral equations for graded anisotropic materials.

MSC:
35A08 Fundamental solutions to PDEs
80M15 Boundary element methods applied to problems in thermodynamics and heat transfer
80A20 Heat and mass transfer, heat flow (MSC2010)
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