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The exact boundary controllability of linear and nonlinear Korteweg-de
Vries equation on bounded domains with various boundary conditions is
studied. When boundary conditions bear on spatial derivatives up to
order 2, the exact controllability result by Russell-Zhang is directly
proved by means of Hilbert Uniqueness Method. When only the first
spatial derivative at the right endpoint is assumed to be controlled,
a quite different analysis shows that exact controllability holds too.
From...
We prove the exact boundary controllability of the 3-D Euler equation
of incompressible inviscid fluids on a regular connected bounded open set when the
control operates on an open part of the boundary that
meets any of the connected components of the boundary.
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.
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.
We study the boundary controllability of a nonlinear Korteweg–de Vries equation with the Dirichlet boundary condition on an interval with a critical length for which it has been shown by Rosier that the linearized control system around the origin is not controllable. We prove that the nonlinear term gives the local controllability around the origin.
We study the exact boundary controllability of two coupled one dimensional wave equations with a control acting only in one equation. The problem is transformed into a moment problem. This framework has been used in control theory of distributed parameter systems since the classical works of A.G. Butkovsky, H.O. Fattorini and D.L. Russell in the late 1960s to the early 1970s. We use recent results on the Riesz basis property of exponential divided differences.
Several kinds of exact synchronizations and the generalized exact synchronization are introduced for a coupled system of 1-D wave equations with various boundary conditions and we show that these synchronizations can be realized by means of some boundary controls.
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