Geodesic
A problem with displacements in the boundary conditions
Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, no. 8 (2011), pp. 102-107

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A problem with conditions relating to the values of an unknown function on the opposite sides of a rectangular characteristiс domain D for a linear hyperbolic equations is considered. This problem is reduced to the system of Fredholm equations of the second kind. The proof of solvability is based on the a priori estimates of additional conditions on the coefficients of the equation.
Keywords: problems with displacements, hyperbolic equation, Fredholm equations. 
@article{VSGU_2011_8_a10,
     author = {E. A. Utkina},
     title = {A problem with displacements in the boundary conditions},
     journal = {Vestnik Samarskogo universiteta. Estestvennonau\v{c}na\^a seri\^a},
     pages = {102--107},
     publisher = {mathdoc},
     number = {8},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VSGU_2011_8_a10/}
}
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E. A. Utkina. A problem with displacements in the boundary conditions. Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, no. 8 (2011), pp. 102-107. http://geodesic.mathdoc.fr/item/VSGU_2011_8_a10/