1,969 research outputs found

    Controllability results for some nonlinear coupled parabolic systems by one control force

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    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

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    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

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    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

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    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

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    In this paper, we consider the well-known Fattorini's criterion for approximate controllability of infinite dimensional linear systems of type y′=Ay+Buy'=A y+Bu. We precise the result proved by H. O. Fattorini in \cite{Fattorini1966} for bounded input BB, in the case where BB 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 AA 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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