Abstract
The one-dimensional semilinear heat equation\(\frac{{\partial y}}{{\partial t}} = \frac{{\partial ^2 y}}{{\partial x^2 }} + F(y) + bu(t)\) is considered. It is shown that if the nonlinear functionF(y) is uniformly bounded then the system is approximately controllable for every given terminal timeT>0 under some ordinary condition onb. The results may be extended to the general one-dimensional semilinear heat equation with one-dimensional control or to a boundary control heat system with semilinear boundary condition.
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Communicated by A. V. Balakrishnan
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Hong, X.Z. A note on approximate controllability for semilinear one-dimensional heat equation. Appl Math Optim 8, 275–285 (1982). https://doi.org/10.1007/BF01447763
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DOI: https://doi.org/10.1007/BF01447763