We consider the wave equation with a time-varying delay term in the boundary condition in a bounded and smooth domain Ω ⊂ IRn . Under suitable assumptions, we prove exponential stability of the solution. These results are obtained by introducing suitable energies and suitable Lyapunov functionals. Such analysis is also extended to a nonlinear version of the model.

Exponential stability of the wave equation with boundary time-varying delay

PIGNOTTI, CRISTINA;
2011

Abstract

We consider the wave equation with a time-varying delay term in the boundary condition in a bounded and smooth domain Ω ⊂ IRn . Under suitable assumptions, we prove exponential stability of the solution. These results are obtained by introducing suitable energies and suitable Lyapunov functionals. Such analysis is also extended to a nonlinear version of the model.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11697/12553
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