Name
Title | ||
|---|---|---|
Stability and Instability Results of the Wave Equation with a Delay Term in the Boundary or Internal Feedbacks |
Abstract | ||
|---|---|---|
In this paper we consider, in a bounded and smooth domain, the wave equation with a delay term in the boundary condition. We also consider the wave equation with a delayed velocity term and mixed Dirichlet-Neumann boundary condition. In both cases, under suitable assumptions, we prove exponential stability of the solution. These results are obtained by introducing suitable energies and by using some observability inequalities. If one of the above assumptions is not satisfied, some instability results are also given by constructing some sequences of delays for which the energy of some solutions does not tend to zero. |
Year | DOI | Venue |
|---|---|---|
2006 | 10.1137/060648891 | SIAM J. Control and Optimization |
Keywords | Field | DocType |
observability inequality,exponential stability,suitable energy,delay term,wave equation,boundary condition,delayed velocity term,suitable assumption,mixed dirichlet-neumann boundary condition,internal feedbacks,instability results,instability result | Boundary value problem,Mathematical optimization,Dirichlet problem,Mathematical analysis,Exponential stability,Wave equation,Neumann boundary condition,Partial differential equation,Mathematics,Hyperbolic partial differential equation,Mixed boundary condition | Journal |
Volume | Issue | ISSN |
45 | 5 | 0363-0129 |
Citations | PageRank | References |
43 | 7.26 | 1 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Serge Nicaise | 1 | 193 | 35.30 |
| Cristina Pignotti | 2 | 73 | 13.08 |