Boundary controllability of differential equations with nonlocal condition.

*(English)*Zbl 0917.93009Global exact boundary controllability in a given time-interval of a semilinear abstract dynamical system is considered. It is generally assumed that the dynamical system is defined in an infinite-dimensional Banach space, that it contains both a linear and a nonlinear part, and that, moreover, it satisfies the so-called nonlocal conditions. Using a Banach fixed-point theorem, a sufficient condition for exact boundary global controllability is formulated and proved. As an application, boundary exact controllability of certain semilinear distributed parameter dynamical systems with Dirichlet boundary conditions is investigated. Similar controllability problems for semilinear abstract dynamical systems have been recently considered in the paper of the authors and Y.-C. Kwun [Indian. J. Pure Appl. Math. 29, No. 9, 941-950 (1998; Zbl 0917.93008)].

Reviewer: J.Klamka (Katowice)

##### MSC:

93B05 | Controllability |

93C25 | Control/observation systems in abstract spaces |

93C10 | Nonlinear systems in control theory |

##### Keywords:

global exact boundary controllability; semilinear abstract dynamical systems; nonlocal conditions; Banach fixed-point theorem##### Citations:

Zbl 0917.93008
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\textit{H.-K. Han} and \textit{J.-Y. Park}, J. Math. Anal. Appl. 230, No. 1, 242--250 (1999; Zbl 0917.93009)

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##### References:

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