The search session has expired. Please query the service again.
The search session has expired. Please query the service again.
In this work we are interested in the study of controllability and stabilization of the linearized Benjamin-Ono equation with periodic boundary conditions, which is a generic model for the study of weakly nonlinear waves with nonlocal dispersion. It is well known that the Benjamin-Ono equation has infinite number of conserved quantities, thus we consider only controls acting in the equation such that the volume of the solution is conserved. We study also the stabilization with a feedback law which...
In this work we are interested in the study of controllability and
stabilization of the linearized Benjamin-Ono equation with
periodic boundary conditions, which is a generic model for the
study of weakly nonlinear waves with nonlocal dispersion. It is
well known that the Benjamin-Ono equation has infinite number of
conserved quantities, thus we consider only controls acting in the
equation such that the volume of the solution is conserved. We
study also the stabilization with a feedback law...
For boundary or distributed controls, we get an approximate
controllability result for the Navier-Stokes equations in
dimension 2 in the case where the fluid is incompressible
and slips on the boundary in agreement with the Navier slip
boundary conditions.
We present here a return method to describe some attainable sets
on an interval of the classical Burger equation by means of the
variation of the domain.
We study the dynamic behavior and stability of two connected
Rayleigh beams that are subject to, in addition to two sensors and
two actuators applied at the joint point, one of the actuators also
specially distributed along the beams. We show that with the
distributed control employed, there is a set of generalized
eigenfunctions of the closed-loop system, which forms a Riesz basis
with parenthesis for the state space. Then both the
spectrum-determined growth condition and exponential stability...
In this paper, we consider the well-known Fattorini’s criterion for approximate controllability of infinite dimensional linear systems of type y′ = Ay + Bu. We precise the result proved by Fattorini in [H.O. Fattorini, SIAM J. Control 4 (1966) 686–694.] for bounded input B, in the case where B can be unbounded or in the case of finite-dimensional controls. More precisely, we prove that if Fattorini’s criterion is satisfied and if the set of geometric multiplicities of A is bounded then approximate...
This work studies the null-controllability of a class of abstract parabolic
equations. The main contribution in the general case
consists in giving a short proof of an abstract version of a sufficient
condition for null-controllability which has been proposed by Lebeau and
Robbiano. We do not assume that the control operator is admissible.
Moreover, we give estimates of the control cost.
In the special case of the heat equation in rectangular domains, we provide
an alternative way to check...
This work studies the null-controllability of a class of abstract parabolic
equations. The main contribution in the general case
consists in giving a short proof of an abstract version of a sufficient
condition for null-controllability which has been proposed by Lebeau and
Robbiano. We do not assume that the control operator is admissible.
Moreover, we give estimates of the control cost.
In the special case of the heat equation in rectangular domains, we provide
an alternative way to check...
In this paper we show that the set of all mild solutions of the Cauchy problem for a functional-differential inclusion in a separable Banach space E of the form x’(t) ∈ A(t)x(t) + F(t,xt) is an -set. Here A(t) is a family of linear operators and F is a Carathéodory type multifunction. We use the existence result proved by V. V. Obukhovskiĭ [22] and extend theorems on the structure of solutions sets obtained by N. S. Papageorgiou [23] and Ya. I. Umanskiĭ [32].
An open-loop system of a multidimensional wave equation
with variable coefficients, partial boundary Dirichlet control and
collocated observation is considered. It is shown that the system is
well-posed in the sense of D. Salamon and regular in the sense of G.
Weiss. The Riemannian geometry method is used in the proof of
regularity and the feedthrough operator is explicitly computed.
An approximation procedure for time optimal control problems for the linear wave equation is analyzed. Its asymptotic behavior is investigated and an optimality system including the maximum principle and the transversality conditions for the regularized and unregularized problems are derived.
Currently displaying 21 –
40 of
59