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

This paper is devoted to studying the null and approximate controllability of two linear coupled parabolic equations posed on a smooth domain Ω of R N ( N ⩾ 1 ) with coupling terms of zero and first orders and one control localized in some arbitrary nonempty open subset ω of the domain Ω . We prove...

Full description

Saved in:
Bibliographic Details
Published inJournal of evolution equations Vol. 18; no. 2; pp. 659 - 680
Main Authors Duprez, Michel, Lissy, Pierre
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 01.06.2018
Springer Nature B.V
Springer Verlag
Subjects
Analysis
Analysis of PDEs
Controllability
Coupling
Mathematical analysis
Mathematics
Mathematics and Statistics
Optimization and Control
Stability
35K40
Fictitious control method
93B07
93B05
Algebraic solvability
Controllability
Parabolic systems
Online AccessGet full text

Cover

More Information
Summary:This paper is devoted to studying the null and approximate controllability of two linear coupled parabolic equations posed on a smooth domain Ω of R N ( N ⩾ 1 ) with coupling terms of zero and first orders and one control localized in some arbitrary nonempty open subset ω of the domain Ω . We prove the null controllability under a new sufficient condition and we also provide the first example of a not approximately controllable system in the case where the support of one of the nontrivial coupling terms intersects the control domain ω .
ISSN:1424-3199
1424-3202
DOI:10.1007/s00028-017-0415-1