Skip Navigation

IMA Journal of Mathematical Control and Information 2005 22(3):310-320; doi:10.1093/imamci/dni029
This Article
Right arrow Full Text (PDF)
Right arrow Alert me when this article is cited
Right arrow Alert me if a correction is posted
Services
Right arrow Email this article to a friend
Right arrow Similar articles in this journal
Right arrow Alert me to new issues of the journal
Right arrow Add to My Personal Archive
Right arrow Download to citation manager
Right arrowRequest Permissions
Google Scholar
Right arrow Articles by Bárcenas, D.
Right arrow Articles by Sívoli, Z.
Right arrow Search for Related Content
Social Bookmarking
Add to CiteULike   Add to Connotea   Add to Del.icio.us  
What's this?

© The Author 2005. Published by Oxford University Press on behalf of The Institute of Mathematics and its Applications. All rights reserved.

A broad class of evolution equations are approximately controllable, but never exactly controllable

Diomedes Bárcenas, Hugo Leiva and Zoraida Sívoli

Universidad de Los Andes, Departamento de Matemáticas, Mérida 5101, Venezuela

As we have announced in the title of this work, we show that a broad class of evolution equations are approximately controllable but never exactly controllable. This class is represented by the following infinite-dimensional time-varying control system:

z' = A(t)z + B(t)u(t), t > 0, z Z

where Z, U are Banach spaces, the control function u belong to Lp(0, t1; U), t1 > 0, 1 < p < {infty}, B , L{infty} (0, t1; L(U, Z)) and A(t) generates a strongly continuous evolution operator U(t, s) according to Pazy (1983; Semigroups of Linear Operators with Applications to Partial Differential Equations). Specifically, we prove the following statement: If U(t, s) is compact for 0 <= s < t <= t1, then the system can never be exactly controllable on [0, t1]. This class is so large that includes diffusion equations, damped flexible beam equation, some thermoelastic equations, strongly damped wave equations, etc.

Keywords: evolution equations; approximate and exact controllability; compact operators.


Add to CiteULike CiteULike   Add to Connotea Connotea   Add to Del.icio.us Del.icio.us    What's this?




Disclaimer:
Please note that abstracts for content published before 1996 were created through digital scanning and may therefore not exactly replicate the text of the original print issues. All efforts have been made to ensure accuracy, but the Publisher will not be held responsible for any remaining inaccuracies. If you require any further clarification, please contact our Customer Services Department.