Local existence and exponential growth for a semilinear damped wave equation with dynamic boundary conditions
By Stéphane Gerbi, B. Said-Houari. Advances in Differential Equations, 2008
60 citations recorded by the source corpus.
In this paper we consider a multi-dimensional damped semiliear wave equation with dynamic boundary conditions, related to the Kelvin-Voigt damping. We firstly prove the local existence by using the Faedo-Galerkin approximations combined with a contraction mapping theorem. Secondly, the exponential growth of the energy and the $L^p$ norm of the solution is presented.
Subfields: Computational Theory and Mathematics, Control and Systems Engineering, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/e4ea538fba3c3e7431f7c23ce531d36966bf9df9
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In Computational Theory and Mathematics
- Serge Nicaise
- Cristina Pignotti
- Julie Valein
- B. Said-Houari
- Mokhtar Kirane
- Wenjun Liu
- Mohammad M. Kafini
- Salim A. Messaoudi
In Control and Systems Engineering
- Serge Nicaise
- Cristina Pignotti
- Julie Valein
- B. Said-Houari
- Mokhtar Kirane
- Wenjun Liu
- Salim A. Messaoudi
- Mohammad M. Kafini
In Mathematical Physics
- Serge Nicaise
- Cristina Pignotti
- Julie Valein
- Wenjun Liu
- B. Said-Houari
- Mokhtar Kirane
- Salim A. Messaoudi
- Mohammad M. Kafini
Citations in the corpus
- INTERIOR FEEDBACK STABILIZATION OF WAVE EQUATIONS WITH TIME DEPENDENT DELAY (2011, methodology): “See [1, 3, 21, 9] and the references therein for more details.”