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Explicit solutions of nonlocal boundary value problems, containing Bitsadze-Samarskii constraints. (English) Zbl 1227.35127

Summary: In this paper are found explicit solutions of four nonlocal boundary value problems for Laplace, heat and wave equations, with Bitsadze-Samarskii constraints based on non-classical one-dimensional convolutions. In fact, each explicit solution may be considered as a way for effective summation of a solution in the form of nonharmonic Fourier sine-expansion. Each explicit solution, may be used for numerical calculation of the solutions too.

MSC:

35C10 Series solutions to PDEs
35L20 Initial-boundary value problems for second-order hyperbolic equations
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
35J25 Boundary value problems for second-order elliptic equations
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