## Observabilité frontière de l’equation des ondes. (Boundary observability of the wave equation).(English)Zbl 0598.35060

We prove an observability result for the solutions of the wave equation in a bounded domain, vanishing on its boundary. We show that we can find a $$T>0$$ such that the total energy of any solution can be bounded by a constant multiple of the integral over $$\Gamma_ 0\times [0,T]$$ of the square of the normal derivative of the solution, where $$\Gamma_ 0$$ is the subset of the boundary on which the normal vector points away from the origin.

### MSC:

 35L05 Wave equation 35B35 Stability in context of PDEs

### Keywords:

observability result; wave equation; energy