Geodesic
A problem with dynamic nonlocal condition for pseudohyperbolic equation
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 9 (2016), pp. 42-50

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We consider an initial-boundary problem with dynamic nonlocal boundary condition for a pseudohyperbolic fourth-order equation in a cylinder. Dynamic nonlocal boundary condition represents a relation between values of a required solution, its derivatives with respect of spacial variables, second-order derivatives with respect to time variable and an integral term. 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 the Sobolev spaces.
Keywords: dynamic boundary conditions, pseudohyperbolic equation, generalized solution.
Mots-clés : nonlocal conditions 
@article{IVM_2016_9_a3,
     author = {L. S. Pulkina},
     title = {A problem with dynamic nonlocal condition for pseudohyperbolic equation},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {42--50},
     publisher = {mathdoc},
     number = {9},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2016_9_a3/}
}
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L. S. Pulkina. A problem with dynamic nonlocal condition for pseudohyperbolic equation. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 9 (2016), pp. 42-50. http://geodesic.mathdoc.fr/item/IVM_2016_9_a3/