Differential and Integral Equations

Stabilization of the wave equation with boundary or internal distributed delay

Serge Nicaise and Cristina Pignotti

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text


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.

Article information

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

Export citation