IJPAM: Volume 57, No. 1 (2009)

APPLICATIONS OF COSINE FAMILIES FOR
CONTROL THEORY

Tadeusz Kowalski$^1$, Wawrzyniec Sadkowski$^2$
$^{1,2}$Faculty of Mathematics and Information Sciences
Warsaw University of Technology
Pl. Politechniki 1, Warsaw, 00-661, POLAND
$^2$e-mail: wawsad@mini.pw.edu.pl


Abstract.Some equivalent conditions for exact, null-exact and approximate controllability of ``controlled'' abstract second-order Cauchy problems, with $A$ as a generator of strongly cosine continuous family have bee given. It has been also proved that the mixed wave problem is exactly controllable in the space $H_0^1 [0,1]$ but it is only approximately controllable in the space $L_2 [0,1]$.

Received: October 16, 2009

AMS Subject Classification: 93C25

Key Words and Phrases: cosine families, control theory, the exact and approximate controllability of the mixed wave problem

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2009
Volume: 57
Issue: 1