RECENT RESULTS ON THE CONTROLLABILITY OF LINEAR COUPLED PARABOLIC PROBLEMS: A SURVEY

By F. Ammar-Khodja, Assia Benabdallah, Manuel González-Burgos, Luz de Teresa. 2011

178 citations recorded by the source corpus.

This paper tries to summarize recent results on the controllability of systems of (several) parabolic equations. The emphasis is placed on the extension of the Kalman rank condition (for finite dimensional systems of differential equations) to parabolic systems. This question is itself tied with the proof of global Carleman estimates for systems and leads to a wide field of open problems.

Subfields: Computational Theory and Mathematics, Control and Systems Engineering, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/638c12ca0e14675c5edfac7d8be5ea73ed79d956

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In Computational Theory and Mathematics

In Control and Systems Engineering

In Mathematical Physics

Citations in the corpus

Local null controllability of the three-dimensional Navier–Stokes system with a distributed control having two vanishing components (2012, background): “For a recent survey on the controllability of coupled linear parabolic equations, see [5].”
Controllability of Two Coupled Wave Equations on a Compact Manifold (2013, unknown): “The first positive result concerns the case where ω∩O = ∅ (see [5] or [26]).”
Minimal time for the null controllability of parabolic systems: The effect of the condensation index of complex sequences (2014, background): “For a survey of recent results on null controllability (with boundary or distributed controls) in the framework of non-scalar parabolic systems, see [4] and the references therein.”