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

This article is cited in 5 scientific papers (total in 5 papers)

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 1.1520.2014К


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

Full text: PDF file (263 kB)
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English version:
Computational Mathematics and Mathematical Physics, 2016, 56:10, 1778–1792

Bibliographic databases:

UDC: 519.633
Received: 11.10.2015

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  mathscinet  zmath  isi
    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  crossref  mathscinet  zmath  isi
    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  mathnet  crossref  crossref  isi  elib
    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  crossref  isi
    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  crossref  isi
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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