Boundary approximate controllability of some linear parabolic systems

Abstract

This paper focuses on the boundary approximate controllability of two classes of linear parabolic systems, namely a system of $n$ heat equations coupled through constant terms and a $2\times 2$ cascade system coupled by means of a first order partial differential operator with space-dependent coefficients. For each system we prove a sufficient condition in any space dimension and we show that this condition turns out to be also necessary in one dimension with only one control. For the system of coupled heat equations we also study the problem on rectangle, and we give characterizations depending on the position of the control domain. Finally, we exhibit a cascade system for which the distributed controllability holds whereas the boundary controllability does not. The method relies on a general characterization due to H.O. Fattorini.

References in corpus (3)

• On the Fattorini Criterion for Approximate Controllability and Stabilizability of Parabolic Systems
• On the null-controllability of the heat equation in unbounded domains
• Null-controllability for some linear parabolic systems with controls acting on different parts of the domain and its boundary

Cited by in corpus (4)

• Controllability of a 2x2 parabolic system by one force with a space-dependent coupling term of order one
• Positive and negative results on the internal controllability of parabolic equations coupled by zero and first order terms
• Quantitative Fattorini-Hautus test and minimal null control time for parabolic problems
• Boundary null-controllability of two coupled parabolic equations : simultaneous condensation of eigenvalues and eigenfunctions