Geodesic
On one problem with dynamic nonlocal condition for a hyperbolic equation
Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, no. 3 (2015), pp. 44-52

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In this article, boundary value problem for hyperbolic partial differential equation with nonlocal data in an integral of the second kind form is considered. The emergence of dynamic conditions may be due to the presence of a damping device. Existence and uniqueness of generalized solution is proved in a given cylindrical field. There is some limitation on the input data. The uniqueness of generalized solution is proved by apriori estimates. The existence is proved by Galerkin’s method and embedding theorems.
Keywords: hyperbolic equation, nonlocal condition of the second kind, integral conditions, generalized solution, Galerkin method, damping device, dynamic boundary conditions.
Mots-clés : dynamic nonlocal conditions 
@article{VSGU_2015_3_a3,
     author = {A. E. Savenkova},
     title = {On one problem with dynamic nonlocal condition for a hyperbolic equation},
     journal = {Vestnik Samarskogo universiteta. Estestvennonau\v{c}na\^a seri\^a},
     pages = {44--52},
     publisher = {mathdoc},
     number = {3},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VSGU_2015_3_a3/}
}
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A. E. Savenkova. On one problem with dynamic nonlocal condition for a hyperbolic equation. Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, no. 3 (2015), pp. 44-52. http://geodesic.mathdoc.fr/item/VSGU_2015_3_a3/