Initial-boundary value problems for second order systems of partial differential equations (Q2842477)

Necessary conditions for well-posedness of an IBVP to the wave equation on a half plane with initial conditions on \(t=0\) and different types of boundary conditions are investigated first. By means of Laplace and Fourier transforms, the above problem with homogeneous initial data is reduced to a first order system of pseudo-differential equations. Interior and boundary estimates for solution as well as estimates in case homogeneous boundary data, are obtained. The method has been extended to a system of two wave equations coupled trough the boundary conditions and then developed for a general system of \(n\) second order wave equations. Really interesting are the numerical experiments at the end of the paper.