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Zh. Vychisl. Mat. Mat. Fiz., 2019, Volume 59, Number 2, Pages 286–300 (Mi zvmmf10836)  

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

Classical and generalized solutions of a mixed problem for a nonhomogeneous wave equation

A. P. Khromov, V. V. Kornev

Saratov National Research State University, Saratov, 410012 Russia

Abstract: A.N. Krylov's ideas concerning convergence acceleration for Fourier series are used to obtain explicit expressions for the classical solution of a mixed problem for a nonhomogeneous equation and explicit expressions for a generalized solution in the case of arbitrary summable $q(x)$, $\varphi (x)$, $\psi (x)$, and $f(x,t)$ .

Key words: Fourier method, wave equation, summable potential, classical solution, generalized solution.

DOI: https://doi.org/10.1134/S0044466919020091


English version:
Computational Mathematics and Mathematical Physics, 2019, 59:2, 275–289

Bibliographic databases:

UDC: 517.95
Received: 02.05.2018

Citation: A. P. Khromov, V. V. Kornev, “Classical and generalized solutions of a mixed problem for a nonhomogeneous wave equation”, Zh. Vychisl. Mat. Mat. Fiz., 59:2 (2019), 286–300; Comput. Math. Math. Phys., 59:2 (2019), 275–289

Citation in format AMSBIB
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\jour Zh. Vychisl. Mat. Mat. Fiz.
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\pages 286--300
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\pages 275--289
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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. A. P. Khromov, “O klassicheskom reshenii smeshannoi zadachi dlya odnorodnogo volnovogo uravneniya s zakreplennymi kontsami i nulevoi nachalnoi skorostyu”, Izv. Sarat. un-ta. Nov. ser. Ser. Matematika. Mekhanika. Informatika, 19:3 (2019), 280–288  mathnet  crossref  elib
    2. A. P. Khromov, V. V. Kornev, “Raskhodyaschiesya ryady v metode Fure dlya volnovogo uravneniya”, Tr. IMM UrO RAN, 27, no. 4, 2021, 215–238  mathnet  crossref  elib
    3. I. S. Lomov, “Obobschennaya formula Dalambera dlya telegrafnogo uravneniya”, Materialy 20 Mezhdunarodnoi Saratovskoi zimnei shkoly «Sovremennye problemy teorii funktsii i ikh prilozheniya», Saratov, 28 yanvarya — 1 fevralya 2020 g.  Chast 1, Itogi nauki i tekhn. Ser. Sovrem. mat. i ee pril. Temat. obz., 199, VINITI RAN, M., 2021, 66–79  mathnet  crossref
    4. G. V. Khromova, “Ob operatorakh s razryvnoi oblastyu znachenii i ikh primenenii”, Materialy 20 Mezhdunarodnoi Saratovskoi zimnei shkoly «Sovremennye problemy teorii funktsii i ikh prilozheniya», Saratov, 28 yanvarya — 1 fevralya 2020 g.  Chast 2, Itogi nauki i tekhn. Ser. Sovrem. mat. i ee pril. Temat. obz., 200, VINITI RAN, M., 2021, 58–64  mathnet  crossref
    5. V. P. Kurdyumov, A. P. Khromov, “Raskhodyaschiesya ryady i smeshannaya zadacha dlya volnovogo uravneniya so svobodnymi kontsami”, Materialy 20 Mezhdunarodnoi Saratovskoi zimnei shkoly «Sovremennye problemy teorii funktsii i ikh prilozheniya», Saratov, 28 yanvarya — 1 fevralya 2020 g.  Chast 2, Itogi nauki i tekhn. Ser. Sovrem. mat. i ee pril. Temat. obz., 200, VINITI RAN, M., 2021, 65–72  mathnet  crossref
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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