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A mixed problem for an inhomogeneous wave equation with fixed ends in the case of a summable potential is studied. Using the Krylov method for acceleration of the convergence of Fourier series, a classical solution under minimal conditions on the initial data and a generalized solution in the case of quadratic summable initial data and perturbing function are obtained. [ABSTRACT FROM AUTHOR]

Under minimum smoothness requirements for the initial data, the Fourier method in the mixed problem for the wave equation with a complex potential is justified by using the Cauchy-Poincare technique for the contour integration of the resolvent of the eigenvalue problem. Generic boundary conditions are used; one of them contains first-order derivatives, while the other does not. In this case, even for the benchmark situation, the operator in the eigenvalue problem can have any number of generalized eigenfunctions. A substantial use is made of the technique for accelerating Fourier series due to A.N. Krylov. [ABSTRACT FROM AUTHOR]

The resolvent approach to the Fourier method is used to examine the behavior of the formal solution to the mixed problem for an inhomogeneous wave equation with a summable potential. A classical solution is obtained under minimum conditions imposed on the initial function. It is shown that, in the case of square summable initial and driving functions, the series sum of the formal solution is a weak solution of the mixed problem. [ABSTRACT FROM AUTHOR]