Abstract:
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.
Citation:
A. B. Beylin, L. S. Pulkina, “A problem with dynamical boundary condition for a one-dimensional hyperbolic equation”, Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 24:3 (2020), 407–423
This publication is cited in the following 2 articles:
Abdelbaki Choucha, Salah Boulaaras, Mohammad Alnegga, “Local existence and blow up for the wave equation with nonlinear logarithmic source term and nonlinear dynamical boundary conditions combined with distributed delay”, Afr. Mat., 35:3 (2024)
Nazlı Irk{\i}l, Khaled Mahdi, Erhan Pişkin, Mohammad Alnegga, Salah Boulaaras, “On a logarithmic wave equation with nonlinear dynamical boundary conditions: local existence and blow-up”, J Inequal Appl, 2023:1 (2023)
Citation in format AMSBIB
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