Abstract
For the Cauchy problem associated with a controlled semilinear evolution equation with an operator (not necessarily bounded) in a Hilbert space, we obtain sufficient conditions for exact controllability into a given terminal state (and also into given intermediate states at interim time moments) on an arbitrarily fixed (without additional constraints) time interval. Here we use the Browder—Minty theorem and also a chain technology of successive continuation of the solution of the controlled system to intermediate states. As examples, we consider a semilinear pseudoparabolic equation and a semilinear wave equation.
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Translated by V. Potapchouck
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Chernov, A.V. On the Exact Global Controllability of a Semilinear Evolution Equation. Diff Equat 60, 374–392 (2024). https://doi.org/10.1134/S0012266124030091
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DOI: https://doi.org/10.1134/S0012266124030091