# On a Mixed Boundary Value Problem for the Biharmonic Equation in a Strip

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## 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.

## Keywords

Biharmonic equation Mixed boundary value problems Dual integral equations## Mathematics Subject Classification (2010)

45H05 42A38 46F05 46F10 47G30## Notes

### Acknowledgments

The author would like to thank the referee for valuable comments and suggestions for the original manuscript.

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