Dirichlet, Neumann and mixed Dirichlet-Neumann boundary value problems for Uxy = 0 in rectangles
Ali I. Abdul-Latif · Proceedings of the Royal Society of Edinburgh Section A Mathematics · 1978
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.