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Doklady Rossijskoj Akademii Nauk. Mathematika, Informatika, Processy Upravlenia, 2021, Volume 499, Pages 31–34
DOI: https://doi.org/10.31857/S2686954321040093 (Mi danma185) 		 
This article is cited in 1 scientific paper (total in 1 paper)

MATHEMATICS

On the correct solvability of the Dirichlet boundary value problem for the generalized Helmholtz equation in a strip

V. A. Kostina, D. V. Kostinab, A. V. Kostina

a Voronezh State University, Voronezh, Russia
b Voronezh State Pedagogical University, Voronezh, Russia
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DOI: https://doi.org/10.31857/S2686954321040093
Abstract: Within the framework of the theory of operator cosine functions and its application, a solution of the Dirichlet boundary value problem for the generalized Helmholtz equation in a strip is found and the correct solvability of this problem is established. The critical width of the strip is found depending on the boundary conditions. Applying this result to the problem of heat propagation in a dihedral angle allows us to determine the angle of correctness of this problem and specify the law of heat propagation in the considered region.
Keywords: strongly continuous cosine functions and transformation semigroups, boundary value problems, correct solvability.
Funding agency Grant number
Ministry of Education and Science of the Russian Federation FZGF-2020-0009
This research was supported by the Ministry of Science and Higher Education of the Russian Federation within the state assignment in science, subject no. FZGF-2020-0009.
Presented: V. P. Maslov
Received: 27.04.2021
Revised: 04.06.2021
Accepted: 15.06.2021
English version:
Doklady Mathematics, 2021, Volume 104, Issue 1, Pages 184–187
DOI: https://doi.org/10.1134/S1064562421040098
Bibliographic databases:
Document Type: Article
UDC: 517.9
Language: Russian
Citation: V. A. Kostin, D. V. Kostin, A. V. Kostin, “On the correct solvability of the Dirichlet boundary value problem for the generalized Helmholtz equation in a strip”, Dokl. RAN. Math. Inf. Proc. Upr., 499 (2021), 31–34; Dokl. Math., 104:1 (2021), 184–187
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/danma/v499/p31
    • This publication is cited in the following 1 articles:
    1. V. A. Kostin, D. V. Kostin, M. N. Silaeva, A. P. Zhurikhin, “On the solvability of the Cauchy problem for the wave equation of aerodynamics describing the supersonic flow of thin surfaces”, Lobachevskii J. Math., 44:8 (2023), 3398  crossref  mathscinet
    Citing articles in Google Scholar: Russian citations, English citations
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    		Doklady Rossijskoj Akademii Nauk. Mathematika, Informatika, Processy Upravlenia Doklady Rossijskoj Akademii Nauk. Mathematika, Informatika, Processy Upravlenia
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    Abstract page:138
    Full-text PDF :45
    References:24
     
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