On a Mixed Boundary Value Problem for the Biharmonic Equation in a Strip
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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.
KeywordsBiharmonic equation Mixed boundary value problems Dual integral equations
Mathematics Subject Classification (2010)45H05 42A38 46F05 46F10 47G30
The author would like to thank the referee for valuable comments and suggestions for the original manuscript.
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