A problem with dynamic nonlocal condition for pseudohyperbolic equation

L. S. Pulkina

Izvestiâ vysših učebnyh zavedenij. Matematika, no. 9 (2016), pp. 42-50.

Résumé

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.

Détail

Keywords: dynamic boundary conditions, pseudohyperbolic equation, generalized solution.
Mots-clés : nonlocal conditions

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