Geodesic
Problem with dynamic boundary conditions for a hyperbolic equation
Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, no. 1 (2017), pp. 21-27

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We consider an initial-boundary problem with dynamic boundary condition for a hyperbolic equation in a rectangle. Dynamic boundary condition represents a relation between values of derivatives with respect of spacial variables of a required solution and first-order derivatives with respect to time variable. The main result lies in substantiation of solvability of this problem. We prove the existence and uniqueness of a generalized solution. The proof is based on the a priori estimates obtained in this paper, Galyorkin’s procedure and the properties of Sobolev spaces.
Keywords: dynamic boundary conditions, hyperbolic equation, generalized solution. 
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     author = {V. A. Kirichek and L. S. Pulkina},
     title = {Problem with dynamic boundary conditions for a hyperbolic equation},
     journal = {Vestnik Samarskogo universiteta. Estestvennonau\v{c}na\^a seri\^a},
     pages = {21--27},
     publisher = {mathdoc},
     number = {1},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VSGU_2017_1_a2/}
}
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V. A. Kirichek; L. S. Pulkina. Problem with dynamic boundary conditions for a hyperbolic equation. Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, no. 1 (2017), pp. 21-27. http://geodesic.mathdoc.fr/item/VSGU_2017_1_a2/