Energy Decay Rate of Wave Equations with Indefinite Damping
By Ahmed Benaddi, Bopeng Rao. 2000
62 citations recorded by the source corpus.
Abstract We consider the one-dimensional wave equation with an indefinite sign damping and a zero order potential term. Using a shooting method, we establish the asymptotic expansion of eigenvalues and eigenvectors of the damped wave equation for a large class of coefficients. In addition, if the damping coefficient is “more positive than negative,” we prove that the energy of system decays uniformly exponentially to zero. This sharp result generalizes a previous work of Freitas and Zuazua (1996).
Subfields: Computational Theory and Mathematics, Control and Systems Engineering, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/f800fb48a8f8ae60ea6f265e242e1a35d54fc137
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In Computational Theory and Mathematics
- J. E. Muñoz Rivera
- Reinhard Racke
- Salim A. Messaoudi
- Muhammad I. Mustafa
- Hao Wu
- Tijani Abdul-Aziz Apalara
In Control and Systems Engineering
- J. E. Muñoz Rivera
- Reinhard Racke
- Salim A. Messaoudi
- Aissa Guesmia
- Mauro L. Santos
- Muhammad I. Mustafa
- Abdelfeteh Fareh
- Mohammad M. Kafini
In Mathematical Physics
- J. E. Muñoz Rivera
- Reinhard Racke
- Salim A. Messaoudi
- Aissa Guesmia
- Shuichi Kawashima
- Muhammad I. Mustafa
- Abdelfeteh Fareh
- Mohammad M. Kafini
Citations in the corpus
- Timoshenko systems with indefinite damping (2008, methodology): “K. Liu, Z. Liu and Rao [10] gave an abstract treatment of these results under certain conditions on the abstract damping operator.”