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Steady heat conduction of a material with an array of cylindrical holes in the nonlinear case. (English) Zbl 0914.35043

Summary: We consider steady heat conduction of a material with an array of cylindrical holes. We assume that the thermal conductivity of the material depends on temperature. Using complex potentials we reduce the problem to the Hilbert boundary-value problem in a class of doubly periodic functions. The last problem is solved in closed form by a method of functional equations. Approximate and exact analytical formulae for the effective conductivity tensor are deduced.

MSC:

35J25 Boundary value problems for second-order elliptic equations
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
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