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Boundary controllability of differential equations with nonlocal condition. (English) Zbl 0917.93009
Global 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)].

MSC:
93B05 Controllability
93C25 Control/observation systems in abstract spaces
93C10 Nonlinear systems in control theory
Citations:
Zbl 0917.93008
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References:
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