Geodesic
Solution of certain problem with nonlocal boundary condition for one-dimensional wave equation
Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, Tome 30 (2024) no. 3, pp. 17-24 Cet article a éte moissonné depuis la source Math-Net.Ru

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In this paper, we study a problem with nonlocal boundary condition for one-dimensional wave equation. To prove the solvability of the problem we construct biortogonal basis consisting of eigen- and adjoint-functions of not self adjoint operator.
Keywords: wave equation, boundary problem
Mots-clés : nonlocal condition, biortogonal basis. 
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E. E. Gasanova; L. S. Pulkina. Solution of certain problem with nonlocal boundary condition for one-dimensional wave equation. Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, Tome 30 (2024) no. 3, pp. 17-24. http://geodesic.mathdoc.fr/item/VSGU_2024_30_3_a1/

[1] Samarskii A.A., “O nekotorykh problemakh teorii differentsialnykh uravnenii”, Differentsialnye uravneniya, 16:11 (1980), 1925–1935 | MR

[2] Ba\v{za}nt Zdeněk P., Jirásek Milan, “Nonlocal Integral Formulation of Plasticity And Damage: Survey of Progress”, Journal of Engineering Mechanics, 128:11 (2002), 1119–1149 | DOI

[3] Steklov V.A., “Zadacha ob okhlazhdenii neodnorodnogo tverdogo sterzhnya”, Soobsch. Kharkovskogo mat. obschestva. Vtoraya seriya, 5:3-4 (1897), 136–181 | MR

[4] Ionkin N.I., “Reshenie odnoi kraevoi zadachi teorii teploprovodnosti s neklassicheskim kraevym usloviem”, Differentsialnye uravneniya, 13:2 (1977), 294–304 | MR | Zbl

[5] Beilin S.A., “Existence of solutions for one-dimensional wave equations with nonlocal conditions”, Electronic Journal of Differential Equations, 2001:76 (2001), 1–8 https://ejde.math.txstate.edu/Volumes/2001/76/beilin.pdf | MR

[6] Nakhushev A.M., Zadachi so smescheniem dlya uravnenii v chastnykh proizvodnykh, Nauka, M., 2006, 287 pp. https://knigogid.ru/books/1900983-zadachi-so-smescheniem-dlya-uravneniy-v-chastnyh-proizvodnyh/toread

[7] Pulkina L.S., “Nonlocal problems for hyperbolic equations from the viewpoint of strongly regular boundary conditions”, Electronic Journal of Differential Equations, 2020:28 (2020), 1–20 https://ejde.math.txstate.edu/Volumes/2020/28/pulkina.pdf

[8] Ilin V.A., “Neobkhodimye i dostatochnye usloviya bazisnosti podsistemy sobstvennykh i prisoedinennykh funktsii puchka M.V. Keldysha obyknovennykh differentsialnykh operatorov”, Doklady Akademii nauk SSSR, 227:4 (1976), 796–799 | MR | Zbl

[9] Ilin V.A., “O bezuslovnoi bazisnosti na zamknutom intervale sistem sobstvennykh i prisoedinennykh funktsii differentsialnogo operatora 2 poryadka”, Doklady Akademii nauk SSSR, 273:5 (1983), 1048–1053 | MR | Zbl