Geodesic
A Mixed Problem with Integral Condition for the Hyperbolic Equation
Matematičeskie zametki, Tome 74 (2003) no. 3, pp. 435-445 Cet article a éte moissonné depuis la source Math-Net.Ru

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In this paper, we study a mixed problem for the hyperbolic equation with a boundary Neumann condition and a nonlocal integral condition. We justify the assertion that there exists a unique generalized solution of the problem under consideration. The proof of uniqueness is based on an estimate, derived a priori, in the function space introduced in the paper, while the existence of a generalized solution is proved by the Galerkin method. 
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     author = {L. S. Pulkina},
     title = {A {Mixed} {Problem} with {Integral} {Condition} for the {Hyperbolic} {Equation}},
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L. S. Pulkina. A Mixed Problem with Integral Condition for the Hyperbolic Equation. Matematičeskie zametki, Tome 74 (2003) no. 3, pp. 435-445. http://geodesic.mathdoc.fr/item/MZM_2003_74_3_a11/

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

[2] Cannon J. R., “The solution of the heat equation subject to the specification of energy”, Quart. Appl. Math., 21 (1963), 155–160 | MR

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

[4] Nakhushev A. M., “Ob odnom priblizhennom metode resheniya kraevykh zadach dlya differentsialnykh uravnenii i ego prilozheniya k dinamike pochvennoi vlagi i gruntovykh vod”, Differents. uravneniya, 18:1 (1982), 72–81 | MR | Zbl

[5] Gordeziani D. G., Avalishvili G. A., “Resheniya nelokalnykh zadach dlya odnomernykh kolebanii sredy”, Matem. modelir., 12:1 (2000), 94–103 | MR | Zbl

[6] Bouziani A., “Solution forte d'un problème mixte avec conditions non locales pour une classe d'equations hyperboliques”, Bull. Cl. Sci. Acad. Roy. Belg., 8 (1997), 53–70 | MR

[7] Beilin S., “Existence of solutions for one-dimensional wave equations with nonlocal conditions”, Electronic J. of Diff. Equations, 76 (2001), 1–8 | MR

[8] Gording L., Zadacha Koshi dlya giperbolicheskikh uravnenii, IL, M., 1961