Differential and Integral Equations

Stabilization of the wave equation with boundary or internal distributed delay

Serge Nicaise and Cristina Pignotti

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Abstract

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

Source
Differential Integral Equations, Volume 21, Number 9-10 (2008), 935-958.

Dates
First available in Project Euclid: 20 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.die/1356038593

Mathematical Reviews number (MathSciNet)
MR2483342

Zentralblatt MATH identifier
1224.35247

Subjects
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

Citation

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


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