Tsankov, Yulian Ts. Explicit solutions of nonlocal boundary value problems, containing Bitsadze-Samarskii constraints. (English) Zbl 1227.35127 Fract. Calc. Appl. Anal. 13, No. 4, 435-446 (2010). 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. Cited in 1 Document 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 Keywords:extended Duhamel principle; associated eigenfunctions; non-classical one-dimensional convolutions; nonharmonic Fourier sine-expansion PDFBibTeX XMLCite \textit{Y. Ts. Tsankov}, Fract. Calc. Appl. Anal. 13, No. 4, 435--446 (2010; Zbl 1227.35127) Full Text: EuDML