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Dirichlet, Neumann and mixed Dirichlet-Neumann boundary value problems for Uxy = 0 in rectangles

Published online by Cambridge University Press:  14 November 2011

Ali I. Abdul-Latif
Ali I. Abdul-Latif
Affiliation:
Al-Fateh University, Tripoli, Libya
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Synopsis

It is well known that the Dirichlet problem for hyperbolic equations is a classical “not well posed” problem. Here we consider the Dirichlet, Neumann and mixed Dirichlet-Neumann boundary value problems for the hyperbolic equation uxy = 0 in all positions of the square and a class of rectangles. We also get a partial answer to the problem which deals with a ray that moves from any point on the boundary of a rectangle and is reflected on the boundary such that the angle between every ray and its reflection is π/2.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 82 , Issue 1-2 , 1978 , pp. 107 - 110
Copyright
Copyright © Royal Society of Edinburgh 1978

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