Investigating the Existence of Solution for the Initial non-Local Boundary Value Problem of the Wave

In this paper, we seek to find the classical solution to the initial-boundary value problem involving the partial differential equation of the wave. Since the spectral problem of the wave equation has no eigenvalues or the eigenvalues cover the whole complex plane as a whole, the separable method cannot be used. We also cannot use the Laplace transform method because divergent integrals appear in the inverse Laplace transform. Therefore, we use the characteristic method to find the solution.

Keywords:

Initial boundary value problem , Method of characteristics , Necessary conditions , Classical solution