1,969 research outputs found
Controllability results for some nonlinear coupled parabolic systems by one control force
In this paper, we present new controllability results for some nonlinear
coupled parabolic systems considered in a bounded domain Ω of IRN
(with N ≥ 1 being arbitrary) when the control force acts on a unique
equation of the system through an arbitrarily small open set ω ⊂ Ω. As
a model example, we consider a nonlinear phase field system with certain
superlinear nonlinearities and prove the null controllability, the exact
controllability to the trajectories and the approximate controllability of
the model. The crucial point in this paper is the new strategy developed
to deal with the null controllability of linear coupled parabolic systems
by a unique control force. Global Carleman estimates and the parabolic
regularizing effect of the problem are used.Ministerio de Educación y Cienci
Null controllability of a parabolic system with a cubic coupling term
We consider a system of two parabolic equations with a forcing term present
in one equation and a cubic coupling term in the other one. We prove that the
system is locally null controllable.Comment: 24 page
A parabolic approach to the control of opinion spreading
We analyze the problem of controlling to consensus a nonlinear system
modeling opinion spreading. We derive explicit exponential estimates on the
cost of approximately controlling these systems to consensus, as a function of
the number of agents N and the control time-horizon T. Our strategy makes use
of known results on the controllability of spatially discretized semilinear
parabolic equations. Both systems can be linked through time-rescalin
A uniform controllability result for the Keller-Segel system
In this paper we study the controllability of the Keller-Segel system
approximating its parabolic-elliptic version. We show that this parabolic
system is locally uniform controllable around a constant solution of the
parabolic-elliptic system when the control is acting on the component of the
chemical
On the Fattorini Criterion for Approximate Controllability and Stabilizability of Parabolic Systems
In this paper, we consider the well-known Fattorini's criterion for
approximate controllability of infinite dimensional linear systems of type
. We precise the result proved by H. O. Fattorini in
\cite{Fattorini1966} for bounded input , in the case where 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 is bounded then approximate controllability can be
achieved with finite dimensional controls. An important consequence of this
result consists in using the Fattorini's criterion to obtain the feedback
stabilizability of linear and nonlinear parabolic systems with feedback
controls in a finite dimensional space. In particular, for systems described by
partial differential equations, such a criterion reduces to a unique
continuation theorem for a stationary system. We illustrate such a method by
tackling some coupled Navier-Stokes type equations (MHD system and micropolar
fluid system) and we sketch a systematic procedure relying on Fattorini's
criterion for checking stabilizability of such nonlinear systems. In that case,
the unique continuation theorems rely on local Carleman inequalities for
stationary Stokes type systems
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