### Remarks on null controllability for semilinear heat equation in moving domains.

Menezes, S.B., Limaco, J., Medeiros, L.A. (2003)

Electronic Journal of Qualitative Theory of Differential Equations [electronic only]

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Menezes, S.B., Limaco, J., Medeiros, L.A. (2003)

Electronic Journal of Qualitative Theory of Differential Equations [electronic only]

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Saint Jean Paulin, Jeannine, Vanninathan, M. (1994)

Portugaliae Mathematica

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Apolaya, Ricardo Fuentes (1994)

Portugaliae Mathematica

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Jean-Pierre Raymond, Muthusamy Vanninathan (2005)

ESAIM: Control, Optimisation and Calculus of Variations

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A model representing the vibrations of a fluid-solid coupled structure is considered. Following Hilbert Uniqueness Method (HUM) introduced by Lions, we establish exact controllability results for this model with an internal control in the fluid part and there is no control in the solid part. Novel features which arise because of the coupling are pointed out. It is a source of difficulty in the proof of observability inequalities, definition of weak solutions and the proof of controllability...

M. M. Cavalcanti (1999)

Archivum Mathematicum

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In this paper we study the boundary exact controllability for the equation $$\frac{\partial}{\partial t}\left(\alpha \left(t\right)\frac{\partial y}{\partial t}\right)-\sum _{j=1}^{n}\frac{\partial}{\partial {x}_{j}}\left(\beta \left(t\right)a\left(x\right)\frac{\partial y}{\partial {x}_{j}}\right)=0\phantom{\rule{0.277778em}{0ex}}\phantom{\rule{0.277778em}{0ex}}\phantom{\rule{0.277778em}{0ex}}\text{in}\phantom{\rule{0.277778em}{0ex}}\phantom{\rule{0.277778em}{0ex}}\Omega \times (0,T)\phantom{\rule{0.166667em}{0ex}},$$ when the control action is of Dirichlet-Neumann form and $\Omega $ is a bounded domain in ${R}^{n}$. The result is obtained by applying the HUM (Hilbert Uniqueness Method) due to J. L. Lions.

Jacques-Louis Lions, Enrique Zuazua (1996)

ESAIM: Control, Optimisation and Calculus of Variations

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Bopeng Rao (2001)

ESAIM: Control, Optimisation and Calculus of Variations

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We consider the exact controllability of a hybrid system consisting of an elastic beam, clamped at one end and attached at the other end to a rigid antenna. Such a system is governed by one partial differential equation and two ordinary differential equations. Using the HUM method, we prove that the hybrid system is exactly controllable in an arbitrarily short time in the usual energy space.