Acta Mathematica Vietnamica
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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 NGANpp. 375-396
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 $|x| \leq 6$ 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.