Controllability for a nonlinear abstract evolution equation. (English. Russian original) Zbl 1063.93008

Rozanova, A. V.

Math. Notes 76, No. 4, 511-524 (2004); translation from Mat. Zametki 76, No. 4, 553-567 (2004).

Summary: We prove a theorem on the local controllability of a system described by a nonlinear evolution equation in Banach space when the control is a multiplier on the right-hand side. We obtain sufficient conditions on the size of the neighborhood from which we can take the function from the overdetermination condition so that the inverse problem is uniquely solvable.

MSC:

93B05	Controllability
47N70	Applications of operator theory in systems, signals, circuits, and control theory
93C25	Control/observation systems in abstract spaces

Keywords:

Cauchy problem; Fréchet derivative; local controllability; nonlinear evolution equation