Mixed Problem for a Homogeneous Wave Equation with a Nonzero Initial Velocity


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Abstract

A mixed problem for a homogeneous wave equation with fixed ends, a summable potential, and a nonzero initial velocity is studied. Using the resolvent approach and developing the Krylov method for accelerating the convergence of Fourier series, a classical solution is obtained by the Fourier method under minimal conditions on the smoothness of the initial data and a generalized solution in the case of the initial velocity represented by an arbitrary summable function is found.

About the authors

A. P. Khromov

Saratov State University

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Email: KhromovAP@info.sgu.ru
Russian Federation, Saratov, 410012

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