Pierre Lissy

Indirect controllability of some linear parabolic systems of m equations with m − 1 controls involving coupling terms of zero or first order

This paper is devoted to the study of the null and approximate controllability for some classes of linear coupled parabolic systems with less controls than equations. More precisely, for a given bounded domain Ω in R N (N ∈ N *), we consider a system of m linear parabolic equations (m 2) with coupling terms of first and zero order, and m − 1 controls localized in some arbitrary nonempty open subset ω of Ω. In the case of constant coupling coefficients, we provide a necessary and sufficient condition to obtain the null or approximate controllability in arbitrary small time. In the case m = 2 and N = 1, we also give a generic sufficient condition to obtain the null or approximate controllability in arbitrary small time for general coefficients depending on the space and times variables, provided that the supports of the coupling terms intersect the control domain ω. The results are obtained thanks to the fictitious control method together with an algebraic method and some appropriate Carleman estimates.

On the Cost of Fast Controls for Some Families of Dispersive or Parabolic Equations in One Space Dimension

In this paper, we consider the cost of fast controls for a large class of linear equations of parabolic or dispersive type in one space dimension in small time. By extending the work of Tenenbaum and Tucsnak [J. Differential Equations, 243 (2007), pp. 70--100], we are able to give precise upper bounds on the time-dependance of the cost of fast controls when the time of control

Positive and negative results on the internal controllability of parabolic equations coupled by zero- and first-order terms

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A Kalman rank condition for the indirect controllability of coupled systems of linear operator groups

tends to

Addendum to “Local Controllability of the Two-Link Magneto-Elastic Microswimmer”

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Optimal filtration for the approximation of boundary controls for the one-dimensional wave equation using a finite-difference method

. We also give a lower bound of the cost of fast controls for the same class of equations, which proves the optimality of the power of

Local null controllability of the three-dimensional Navier–Stokes system with a distributed control having two vanishing components

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A link between the cost of fast controls for the 1-D heat equation and the uniform controllability of a 1-D transport-diffusion equation

involved in the cost of the control. These general results are then applied to treat notably the case of linear KdV equations and fractional heat or Schrodinger equations.

Explicit lower bounds for the cost of fast controls for some 1-D parabolic or dispersive equations, and a new lower bound concerning the uniform controllability of the 1-D transport–diffusion equation

This paper is devoted to studying the null and approximate controllability of two linear coupled parabolic equations posed on a smooth domain