Geodesic
On the Solvability of Certain Spatially Nonlocal Boundary-Value Problems for Linear Hyperbolic Equations of Second Order
Matematičeskie zametki, Tome 90 (2011) no. 2, pp. 254-268 Cet article a éte moissonné depuis la source Math-Net.Ru

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The present paper studies the solvability of spatially nonlocal boundary-value problems with Samarskii boundary condition with variable coefficients for linear hyperbolic equations of second order in the one-dimensional case. In the case of boundary conditions with constant coefficients for the equation $$ u_{tt}-u_{xx}+c(x)u=f(x,t), $$ similar problems were studied earlier by other authors; a significant aspect of their papers was the use of the Fourier method, which dictated a special form of the equation as well as the constancy of the coefficients of the boundary conditions. The method used here does not involve such constraints and allows us to study more general problems.
Keywords: linear hyperbolic equation of second order, spatially nonlocal boundary-value problem, Samarskii boundary condition, Young's inequality. 
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A. I. Kozhanov. On the Solvability of Certain Spatially Nonlocal Boundary-Value Problems for Linear Hyperbolic Equations of Second Order. Matematičeskie zametki, Tome 90 (2011) no. 2, pp. 254-268. http://geodesic.mathdoc.fr/item/MZM_2011_90_2_a7/

[1] A. I. Kozhanov, “O razreshimosti nekotorykh prostranstvenno nelokalnykh kraevykh zadach dlya lineinykh parabolicheskikh uravnenii”, Vestn. Sam. gos. tekhn. un-ta. Estestvennonauchn. seriya, 2008, no. 3(62), 165–174 | MR

[2] N. L. Lazhetich, “O klassicheskoi razreshimosti smeshannoi zadachi dlya odnomernogo giperbolicheskogo uravneniya vtorogo poryadka”, Differents. uravneniya, 42:8 (2006), 1072–1077 | MR | Zbl

[3] A. M. Nakhushev, Uravneniya matematicheskoi biologii, Vysshaya shkola, M., 1995 | Zbl

[4] M. T. Dzhenaliev, K teorii lineinykh kraevykh zadach dlya nagruzhennykh differentsialnykh uravnenii, ITPM NAN RK, Almaty, 1995

[5] S. Ya. Yakubov, Lineinye differentsialno-operatornye uravneniya i ikh prilozheniya, Elm, Baku, 1985 | Zbl

[6] V. A. Trenogin, Funktsionalnyi analiz, Fizmatlit, M., 2007 | MR | Zbl

[7] A. I. Kozhanov, “Ob odnoi nelokalnoi kraevoi zadache s peremennymi koeffitsientami dlya uravnenii teploprovodnosti i Allera”, Differents. uravneniya, 40:6 (2004), 763–774 | MR | Zbl

[8] A. I. Kozhanov, L. S. Pulkina, “O razreshimosti kraevoi zadachi s nelokalnym granichnym usloviem integralnogo vida dlya mnogomernykh giperbolicheskikh uravnenii”, Differents. uravneniya, 42:9 (2006), 1166–1179 | MR | Zbl