Null-controllability of some reaction–diffusion systems with one control force

By F. A. Khodja, Assia Benabdallah, C. Dupaix. 2006

110 citations recorded by the source corpus.

This work is concerned with the null-controllability of semilinear parabolic systems by a single control force acting on a subdomain.

Subfields: Cell Biology, Computational Theory and Mathematics, Control and Systems Engineering

View Paper: https://www.semanticscholar.org/paper/6f5cb9af5a18369aafa81d6e4f4e324267de240c

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In Cell Biology

In Computational Theory and Mathematics

In Control and Systems Engineering

Citations in the corpus

Carleman estimates for the one-dimensional heat equation with a discontinuous coefficient and applications to controllability and an inverse problem (2007, background): “[2], [ 1 ]). In the case of a boundary control there were no positive answer and there are some counterexamples [13].”
Carleman estimates for parabolic equations and applications (2009, background): “In [6, 39], it is assumed that A11 = A12 = 0, and the proof can be completed by directly substituting v by means of u in ω × (0, T ).”
Indirect controllability of some linear parabolic systems of m equations with m − 1 controls involving coupling terms of zero or first order (2016, background): “We also mention [9], where a result of null controllability is proved in the case of a system of two equations with one control force, with an application to the controllability of a non-linear system of transport-diffusion equations.”
INDIRECT STABILIZATION OF LOCALLY COUPLED WAVE-TYPE SYSTEMS (2012, unknown): “8) is fully solved in the case ωb ∩ ωp = ∅ (see [10,16,17,22]).”
New phenomena for the null controllability of parabolic systems: Minimal time and geometrical dependence (2016, background): “The first results on controllability of coupled parabolic equations (n > 1) have been established in [35, 13, 3, 25].”
Inverse problem for a parabolic system with two components by measurements of one component (2008, methodology): “[ 2 ] and [8], it is assumed that A11 = A12 = 0. In that case, the proof can be completed by directly”
On Carleman estimates for elliptic and parabolic operators. Applications to unique continuation and control of parabolic equations (2012, methodology): “The use of global parabolic Carleman estimates has also allowed to address the controllability of non linear equations such as the Navier-Stokes equations [19,29], the Boussinesq system [20], fluid structure systems [9,30], weakly coupled parabolic systems [12,23,32,33] to cite a few.”
Controllability results for cascade systems of m coupled parabolic PDEs by one control force (2010, unknown): “The results in [1] and [2] have been generalized in [12] (see also [11]) in two directions: on the one hand, there are not restrictions on the dimension N , and on the other hand, the authors consider nonlinearities which depend on the gradient of the state.”