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Completeness of root functions for thermal conduction in a strip with piecewise continuous coefficients. (English) Zbl 0903.73008
Summary: We consider the boundary layer problem associated with the steady thermal conduction problem in a thin laminated plate. Two cases of boundary conditions, Dirichlet and Neumann, are treated in the paper. Transmission conditions across the interfaces should be added since the plate is laminated. The study of the structure of the solution in the matching region of the layer with the basis solution in the plate leads to an eigenvalue problem for a second-order operator pencil with piecewise continuous coefficients and to the corresponding boundary and transmission conditions. Twofold completeness of root functions of the latter problem is proved. The boundary layer term can then be expressed as a combination of these functions.
MSC:
74A15Thermodynamics (mechanics of deformable solids)
80A20Heat and mass transfer, heat flow
35P10Completeness of eigenfunctions, eigenfunction expansions for PD operators