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 Zh. Vychisl. Mat. Mat. Fiz., 2016, Volume 56, Number 10, Pages 1795–1809 (Mi zvmmf10467)

On the convergence of the formal Fourier solution of the wave equation with a summable potential

A. P. Khromov

Saratov State University, Saratov, Russia

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 $u(x,0)=\varphi(x)$ than those required for a classical solution up to the case $\varphi(x)\in L_p[0,1]$ for $p>1$. It is shown that the formal solution series always converges and represents a weak solution of the mixed problem.

Key words: Fourier method, wave equation, mixed problem, resolvent, convergence of a formal solution.

 Funding Agency Grant Number Ministry of Education and Science of the Russian Federation 1.1520.2014Ê

DOI: https://doi.org/10.7868/S0044466916100112

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English version:
Computational Mathematics and Mathematical Physics, 2016, 56:10, 1778–1792

Bibliographic databases:

UDC: 519.633

Citation: A. P. Khromov, “On the convergence of the formal Fourier solution of the wave equation with a summable potential”, Zh. Vychisl. Mat. Mat. Fiz., 56:10 (2016), 1795–1809; Comput. Math. Math. Phys., 56:10 (2016), 1778–1792

Citation in format AMSBIB
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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. M. Burlutskaia, “On a resolvent approach in a mixed problem for the wave equation on a graph”, Mem. Differ. Equ. Math. Phys., 72 (2017), 37–44
2. A. P. Khromov, “Mixed problem for the wave equation with a summable potential and nonzero initial velocity”, Dokl. Math., 95:3 (2017), 273–275
3. A. P. Khromov, “Mixed problem for a homogeneous wave equation with a nonzero initial velocity”, Comput. Math. Math. Phys., 58:9 (2018), 1531–1543
4. Khromov A.P., “Necessary and Sufficient Conditions For the Existence of a Classical Solution of the Mixed Problem For the Homogeneous Wave Equation With An Integrable Potential”, Differ. Equ., 55:5 (2019), 703–717
5. Khromov A.P. Kornev V.V., “Classical and Generalized Solutions of a Mixed Problem For a Nonhomogeneous Wave Equation”, Dokl. Math., 99:1 (2019), 11–13
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