Open AccessPROBLEM WITH DYNAMIC BOUNDARY CONDITIONS FOR A HYPERBOLIC EQUATION
Author(s) -
В. А. Киричек,
Л. С. Пулькина
Publication year - 2017
Publication title -
vestnik samarskogo universiteta. estestvennonaučnaâ seriâ
Language(s) - English
Resource type - Journals
eISSN - 2712-8954
pISSN - 2541-7525
DOI - 10.18287/2541-7525-2017-23-1-21-27
Subject(s) - mathematics , uniqueness , rectangle , sobolev space , boundary value problem , mathematical analysis , boundary (topology) , a priori and a posteriori , variable (mathematics) , hyperbolic partial differential equation , a priori estimate , partial differential equation , geometry , philosophy , epistemology
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.