Abstract
The aim of the present work is to consider a mixed boundary value problem for the biharmonic equation in a strip. The problem may be interpreted as a deflection surface of a strip plate with the edges y=0,y = h having clamped conditions on intervals |x|≥a and hinged support conditions for |x|<a. Using the Fourier transform, the problem is reduced to studying a system of dual integral equations on the edges of the strip. The uniqueness and existence theorems of solution of system of dual integral equations are established in appropriate Sobolev spaces. A method for reducing the dual integral equation to infinite system of linear algebraic equations is also proposed.
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Ngoc, N.V. On a Mixed Boundary Value Problem for the Biharmonic Equation in a Strip. Acta Math Vietnam 42, 395–411 (2017). https://doi.org/10.1007/s40306-016-0191-y
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DOI: https://doi.org/10.1007/s40306-016-0191-y