Mixed problem for the wave equation with a summable potential and nonzero initial velocity
- Authors: Khromov A.P.1
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Affiliations:
- Saratov National Research State University
- Issue: Vol 95, No 3 (2017)
- Pages: 273-275
- Section: Mathematics
- URL: https://journals.rcsi.science/1064-5624/article/view/225139
- DOI: https://doi.org/10.1134/S106456241703022X
- ID: 225139
Cite item
Abstract
The resolvent approach in the Fourier method, combined with Krylov’s ideas concerning convergence acceleration for Fourier series, is used to obtain a classical solution of a mixed problem for the wave equation with a summable potential, fixed ends, a zero initial position, and an initial velocity ψ(x), where ψ(x) is absolutely continuous, ψ'(x) ∈ L2[0,1], and ψ(0) = ψ(1) = 0. In the case ψ(x) ∈ L[0,1], it is shown that the series of the formal solution converges uniformly and is a weak solution of the mixed problem.
About the authors
A. P. Khromov
Saratov National Research State University
Author for correspondence.
Email: khromovap@info.sgu.ru
Russian Federation, Saratov, 410012