Dirichlet, Neumann, and mixed boundary value problems for the wave equation u_xx—u_yy=0 for a rectangle

Abstract

We reconsider here a classical “not well posed” problem, the Dirichlet problem for the wave equation for a rectangle with sides parallel to the coordinate axes. For the same domain, we also consider the Neumann, and many mixed Dirichlet–Neumann boundary value problems, including a “general mixed problem” where, at each point which is not a corner, the boundary condition is either of Dirichlet or of Neumann type.

^†The research of this author was supported by the Research Fund of the American University in Cairo, Egypt.

^†The research of this author was supported by the Research Fund of the American University in Cairo, Egypt.

Notes

^†The research of this author was supported by the Research Fund of the American University in Cairo, Egypt.