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A remark on observability of the wave equation with moving boundary

Ammari K., Bchatnia A., El Mufti K.

Journal of Applied Analysis

2017

Vol. 23, nr 1

43--51

We deal with thewave equation with assigned moving boundary (0 < x < a(t)) uponwhich Dirichlet or mixed boundary conditions are specified. Here a(t) is assumed to move slower than light and periodically. Moreover, a is continuous, piecewise linear with two independent parameters. Our major concern will be an observation problem which is based measuring, at each t > 0, of the transverse velocity at a(t). The key to the results is the use of a reduction theorem by Yoccoz [14].

Optimal location of the actuator for the pointwise stabilization at high frequencies of a Bernoulli-Euler beam

Ammari K., Saidi A.

Control and Cybernetics

2002

Vol. 31, no 1

57-66

We consider the optimization of the actuator problem for a Bernoulli-Euler beam. By using Riesz basis theory, we show, at high frequencies, that the optimal location of the actuator is the middle of the beam.