Mityushev, V. Steady heat conduction of a material with an array of cylindrical holes in the nonlinear case. (English) Zbl 0914.35043 IMA J. Appl. Math. 61, No. 1, 91-102 (1998). 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. Cited in 1 ReviewCited in 5 Documents MSC: 35J25 Boundary value problems for second-order elliptic equations 35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation Keywords:complex potentials; Hilbert boundary-value problem; conductivity tensor PDFBibTeX XMLCite \textit{V. Mityushev}, IMA J. Appl. Math. 61, No. 1, 91--102 (1998; Zbl 0914.35043) Full Text: DOI