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Abstract
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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.
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