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Motivated by several works on the stabilization of the oscillator by on-off feedbacks, we study the related problem for the one-dimensional wave equation, damped by an on-off feedback $a\left(t\right)u_t$. We obtain results that are radically different from those known in the case of the oscillator. We consider periodic functions $a$: typically $a$ is equal to $1$ on $(0,T)$, equal to $0$ on $(T,qT)$ and is $qT$-periodic. We study the boundary case and next the locally distributed case, and we give optimal results of stability. In both cases,...

Motivated by several works on the stabilization of the oscillator by on-off feedbacks, we study the related problem for the one-dimensional wave equation, damped by an on-off feedback $a\left(t\right)u_t$. We obtain results that are radically different from those known in the case of the oscillator. We consider periodic functions : typically is equal to on , equal to on and is -periodic. We study the boundary case and next the locally distributed case, and we give . In both cases, we prove that there are of...

Motivated by two recent works of Micu and Zuazua and Cabanillas, De Menezes and Zuazua, we study the null controllability of the heat equation in unbounded domains, typically ${ℝ}_{+}$ or ${ℝ}^N$. Considering an unbounded and disconnected control region of the form $\omega :={\cup }_n{\omega }_n$, we prove two null controllability results: under some technical assumption on the control parts ${\omega }_n$, we prove that every initial datum in some weighted $L^2$ space can be controlled to zero by usual control functions, and every initial datum in $L^2\left(\Omega \right)$ can...

Motivated by two recent works of Micu and Zuazua and Cabanillas, De Menezes and Zuazua, we study the null controllability of the heat equation in unbounded domains, typically ${ℝ}_{+}$ or ${ℝ}^N$. Considering an unbounded and disconnected control region of the form $\omega :={\cup }_n{\omega }_n$, we prove two null controllability results: under some technical assumption on the control parts ${\omega }_n$, we prove that every initial datum in some weighted space can be controlled to zero by usual control functions, and every initial...