Exponential stability of the wave equation withboundary time-varying delay

Abstract

We consider the wave equation with a time-varying delay term inthe boundary condition in a bounded and smooth domain $\Omega\subset\RR^n.$ Under suitableassumptions, 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 versionof the model.