Geodesic
A~problem with dynamical boundary condition for~a~one-dimensional hyperbolic equation
Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, Tome 24 (2020) no. 3, pp. 407-423

Voir la notice de l'article provenant de la source Math-Net.Ru

In this paper, we consider a problem with dynamical boundary conditions for a hyperbolic equation. The dynamical boundary condition is a convenient method to take into account the presence of certain damper when fixing the end of a string or a beam. Problems with dynamical boundary conditions containing first-order derivatives with respect to both space and time variables are not self-ajoint, that complicates solution by spectral analysis. However, these difficulties can be overcome by a method proposed in the paper. The main tool to prove the existence of the unique weak solution to the problem is the priori estimates in Sobolev spaces. As a particular example of the wave equation is considered. The exact solution of a problem with dynamical condition is obtained.
Keywords: hyperbolic equation, boundary-value problem, dynamical boundary condition, weak solution
Mots-clés : Sobolev spaces. 
@article{VSGTU_2020_24_3_a0,
     author = {A. B. Beylin and L. S. Pulkina},
     title = {A~problem with dynamical boundary condition for~a~one-dimensional hyperbolic equation},
     journal = {Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences},
     pages = {407--423},
     publisher = {mathdoc},
     volume = {24},
     number = {3},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VSGTU_2020_24_3_a0/}
}
TY  - JOUR
AU  - A. B. Beylin
AU  - L. S. Pulkina
TI  - A~problem with dynamical boundary condition for~a~one-dimensional hyperbolic equation
JO  - Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences
PY  - 2020
SP  - 407
EP  - 423
VL  - 24
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/VSGTU_2020_24_3_a0/
LA  - ru
ID  - VSGTU_2020_24_3_a0
ER  - 
%0 Journal Article
%A A. B. Beylin
%A L. S. Pulkina
%T A~problem with dynamical boundary condition for~a~one-dimensional hyperbolic equation
%J Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences
%D 2020
%P 407-423
%V 24
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/VSGTU_2020_24_3_a0/
%G ru
%F VSGTU_2020_24_3_a0
A. B. Beylin; L. S. Pulkina. A~problem with dynamical boundary condition for~a~one-dimensional hyperbolic equation. Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, Tome 24 (2020) no. 3, pp. 407-423. http://geodesic.mathdoc.fr/item/VSGTU_2020_24_3_a0/