مشخصات پژوهش

In this paper the wave equation in some non-classic cases has been studied. In the first case boundary conditions are non-local and non- periodic. At that case the associated spectral problem is a self-adjoint problem and consequently the eigenvalues are real. But in the second case the associated spectral problem is non-self-adjoint and consequently the eigenvalues are complex numbers, in which two cases, the solutions of the problem are constructed by the Fourier method. By compatibil- ity conditions and asymptotic expansions of the Fourier coefficients, the convergence of series solutions are proved. Finally, series solutions are established and the uniqueness of the solution is proved by a special way which has not been used in classic texts.