On the Correct Solvability of the Dirichlet Boundary Value Problem for the Generalized Helmholtz Equation in a Strip
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 depe...
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| Veröffentlicht in: | Doklady. Mathematics 2021-07, Vol.104 (1), p.184-187 |
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| container_title | Doklady. Mathematics |
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| creator | Kostin, V. A. Kostin, D. V. Kostin, A. V. |
| description | 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. |
| doi_str_mv | 10.1134/S1064562421040098 |
| format | Article |
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A. ; Kostin, D. V. ; Kostin, A. V.</creator><creatorcontrib>Kostin, V. A. ; Kostin, D. V. ; Kostin, A. V.</creatorcontrib><description>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.</description><identifier>ISSN: 1064-5624</identifier><identifier>EISSN: 1531-8362</identifier><identifier>DOI: 10.1134/S1064562421040098</identifier><language>eng</language><publisher>Moscow: Pleiades Publishing</publisher><subject>Boundary conditions ; Boundary value problems ; Dihedral angle ; Dirichlet problem ; Helmholtz equations ; Mathematics ; Mathematics and Statistics ; Propagation ; Strip ; Trigonometric functions</subject><ispartof>Doklady. Mathematics, 2021-07, Vol.104 (1), p.184-187</ispartof><rights>Pleiades Publishing, Ltd. 2021. ISSN 1064-5624, Doklady Mathematics, 2021, Vol. 104, No. 1, pp. 184–187. © Pleiades Publishing, Ltd., 2021. Russian Text © The Author(s), 2021, published in Doklady Rossiiskoi Akademii Nauk. 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V.</creatorcontrib><title>On the Correct Solvability of the Dirichlet Boundary Value Problem for the Generalized Helmholtz Equation in a Strip</title><title>Doklady. Mathematics</title><addtitle>Dokl. Math</addtitle><description>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.</description><subject>Boundary conditions</subject><subject>Boundary value problems</subject><subject>Dihedral angle</subject><subject>Dirichlet problem</subject><subject>Helmholtz equations</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Propagation</subject><subject>Strip</subject><subject>Trigonometric functions</subject><issn>1064-5624</issn><issn>1531-8362</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2021</creationdate><recordtype>article</recordtype><recordid>eNp1kFFLwzAUhYMoOKc_wLeAz9XcJE3bR51zEwYKU19L2t66jKzZ0lTYfr3dJvggPt0L5zvncg8h18BuAYS8mwNTMlZccmCSsSw9IQOIBUSpUPy033s52uvn5KJtl4zJmDM2IOGloWGBdOS8xzLQubNfujDWhC119UF6NN6UC4uBPriuqbTf0g9tO6Sv3hUWV7R2_gBOsEGvrdlhRadoVwtnw46ON50OxjXUNFTTefBmfUnOam1bvPqZQ_L-NH4bTaPZy-R5dD-LSgEqRBVHUaNWMStigZCUgldpkTBeKZ1BCoVWUpQJIvAygxp5oTTIOuOaSYmyEkNyc8xde7fpsA350nW-6U_mPM5iECrhvKfgSJXeta3HOl97s-rfzIHl-3LzP-X2Hn70tD3bfKL_Tf7f9A2iLnvb</recordid><startdate>20210701</startdate><enddate>20210701</enddate><creator>Kostin, V. A.</creator><creator>Kostin, D. V.</creator><creator>Kostin, A. V.</creator><general>Pleiades Publishing</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>20210701</creationdate><title>On the Correct Solvability of the Dirichlet Boundary Value Problem for the Generalized Helmholtz Equation in a Strip</title><author>Kostin, V. A. ; Kostin, D. V. ; Kostin, A. V.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c316t-d2e3fea650b53e17c32d8b702d6a9181ba643c7ee12c91fe2b6a14f92a044e4d3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2021</creationdate><topic>Boundary conditions</topic><topic>Boundary value problems</topic><topic>Dihedral angle</topic><topic>Dirichlet problem</topic><topic>Helmholtz equations</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Propagation</topic><topic>Strip</topic><topic>Trigonometric functions</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Kostin, V. A.</creatorcontrib><creatorcontrib>Kostin, D. V.</creatorcontrib><creatorcontrib>Kostin, A. V.</creatorcontrib><collection>CrossRef</collection><jtitle>Doklady. 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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.</abstract><cop>Moscow</cop><pub>Pleiades Publishing</pub><doi>10.1134/S1064562421040098</doi><tpages>4</tpages></addata></record> |
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| ispartof | Doklady. Mathematics, 2021-07, Vol.104 (1), p.184-187 |
| issn | 1064-5624 1531-8362 |
| language | eng |
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| subjects | Boundary conditions Boundary value problems Dihedral angle Dirichlet problem Helmholtz equations Mathematics Mathematics and Statistics Propagation Strip Trigonometric functions |
| title | On the Correct Solvability of the Dirichlet Boundary Value Problem for the Generalized Helmholtz Equation in a Strip |
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