Controllability for semilinear control systems of parabolic type
Semilinear, infinite-dimensional, parabolic type control systems are considered. It is generally assumed that the controls are unconstrained and that the abstract differential state equation contains both linear and nonlinear part. Under some general condition of the Lipschitz continuity of the nonlinear term in the state equation, sufficient conditions for approximate global controllability in a given time interval are formulated and proved. In the proofs of the main results, methods of nonlinear functional analysis are extensively used. Finally, a simple example which illustrates the theoretical considerations is given. Remarks and comments concerning approximate controllability of semilinear infinite-dimensional control systems are presented. Similar results can be found e.g. in the paper [\textit{J. Klamka}, Nonlinear Anal. 47, 2939-2949 (2001)].
scientific article; zbMATH DE number 1786045