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...
Saved in:
Published in | Journal of evolution equations Vol. 18; no. 2; pp. 659 - 680 |
---|---|
Main Authors | , |
Format | Journal Article |
Language | English |
Published |
Cham
Springer International Publishing
01.06.2018
Springer Nature B.V Springer Verlag |
Subjects | |
Online Access | Get full text |
Cover
Loading…
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 |