A remark on observability of the wave equation with moving boundary
We deal with the wave equation with assigned moving boundary ($0 0$ of the transverse velocity at $a(t)$. The key to the results is the use of a reduction theorem.
math.AP↗
arXiv subjects
K. El Mufti
Publications and source records attributed to K. El Mufti.
Stabilization of the nonlinear damped wave equation via linear weak observability
We consider the problem of energy decay rates for nonlinearly damped abstract infinite dimensional systems. We prove sharp, simple and quasi-optimal energy decay rates through an indirect method, namely a weak observability estimate for the corresponding undamped system. One of the main advantage of these results is that they allow to combine the optimal-weight convexity method of Alabau-Boussouira and a methodology of Ammari-Tucsnak for weak stabilization by observability. Our results extend to nonlinearly damped systems, those of Ammari and Tucsnak. At the end, we give an appendix on the weak stabilization of linear evolution systems.
math.AP↗