An example of pure stability for the wave equation with moving boundary (Q1276368)

Let \(u(x,t)\) be a solution of the wave equation for \(t\in \mathbb{R}\), \(x\in (0,a(t))\), satisfying some initial data and the following boundary conditions: \(u(0,t)=0\), \(u(a(t),t)=0\), where the moving boundary \(a(t)\) is continuous periodic piecewise linear with no more than two slopes. Using some results of the proceeding paper [\textit{J. Dittrich, J. Duclos} and \textit{N. Gonzales}, Rev. Math. Phys., in press], the author gives the lower and upper bounds of the energy of the field \(u(x,t).\)