Controllability of Some Nonlinear Systems in Hilbert Spaces |
| |
Authors: | J P Dauer N I Mahmudov |
| |
Institution: | (1) University of Tennessee at Chattanooga, Tennessee, USA;(2) Eastern Mediterranean University, Turkey |
| |
Abstract: | In this paper, several abstract results concerning the controllability of semilinear evolution systems are obtained. First, approximate controllability conditions for semilinear systems are obtained by means of a fixed-point theorem of the Rothe type; in this case, the compactness of the linear operator is assumed. Next, the exact controllability of semilinear systems with nonlinearities having small Lipschitz constants is derived by means of the Banach fixed-point theorem; in this case, the compactness of the operators is not assumed. In both cases, it is proven that the controllability of the linear system implies the controllability of the associated semilinear system. Finally, these abstract results are applied to the controllability of the semilinear wave and heat equations. |
| |
Keywords: | Infinite-dimensional systems linear systems controllability fixed-point theorems |
本文献已被 SpringerLink 等数据库收录! |
|