Mixed Problem for a Homogeneous Wave Equation with a Nonzero Initial Velocity
- Authors: Khromov A.P.1
-
Affiliations:
- Saratov State University
- Issue: Vol 58, No 9 (2018)
- Pages: 1531-1543
- Section: Article
- URL: https://journals.rcsi.science/0965-5425/article/view/179862
- DOI: https://doi.org/10.1134/S0965542518090099
- ID: 179862
Cite item
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.
Keywords
About the authors
A. P. Khromov
Saratov State University
Author for correspondence.
Email: KhromovAP@info.sgu.ru
Russian Federation, Saratov, 410012
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