logo_acta

Acta Mathematica Vietnamica

SOLVABILITY OF A SYSTEM OF DUAL INTEGRAL EQUATIONS OF A MIXED BOUNDARY VALUE PROBLEM FOR THE BIHARMONIC EQUATION IN A STRIP

NGUYEN VAN NGOC, NGUYEN THI NGAN

Abstract

The aim of the present work is to consider a mixed boundary value problem of 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|6 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 a solution of the system of dual integral equations are established in appropriate Sobolev spaces. A method for reducing the system of dual integral equations to an infinite system of linear algebraic equations is also proposed.