Email this article On the convergence of the formal Fourier solution of the wave equation with a summable potential
- Authors: Khromov A.P.1
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Affiliations:
- Saratov State University
- Issue: Vol 56, No 10 (2016)
- Pages: 1778-1792
- Section: Article
- URL: https://journals.rcsi.science/0965-5425/article/view/178726
- DOI: https://doi.org/10.1134/S0965542516100110
- ID: 178726
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Abstract
The convergence of the formal Fourier solution to a mixed problem for the wave equation with a summable potential is analyzed under weaker assumptions imposed on the initial position u(x, 0) = φ(x) than those required for a classical solution up to the case φ(x) ∈ Lp[0,1] for p > 1. It is shown that the formal solution series always converges and represents a weak solution of the mixed problem.
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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