Differential and Integral Equations
- Differential Integral Equations
- Volume 21, Number 9-10 (2008), 935-958.
Stabilization of the wave equation with boundary or internal distributed delay
We consider the wave equation in a bounded region with a smooth boundary with distributed delay on the boundary or into the domain. In both cases, under suitable assumptions, we prove the exponential stability of the solution. These results are obtained by introducing suitable energies and by proving some observability inequalities. For an internal distributed delay, we further show some instability results.
Differential Integral Equations, Volume 21, Number 9-10 (2008), 935-958.
First available in Project Euclid: 20 December 2012
Permanent link to this document
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 35L20: Initial-boundary value problems for second-order hyperbolic equations
Secondary: 93C20: Systems governed by partial differential equations 93D15: Stabilization of systems by feedback
Nicaise, Serge; Pignotti, Cristina. Stabilization of the wave equation with boundary or internal distributed delay. Differential Integral Equations 21 (2008), no. 9-10, 935--958. https://projecteuclid.org/euclid.die/1356038593