Controllability of the Semilinear Heat Equation with a Sublinear Term and a Degenerate Actuator

Alexander Y. Khapalov
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Alexander Y. Khapalov: Washington State University, Department of Mathematics and Statistics

Chapter Chapter 5 in Mobile Point Sensors and Actuators in the Controllability Theory of Partial Differential Equations, 2017, pp 63-76 from Springer

Abstract: Abstract In this chapter we study controllability properties of the 1-D semilinear heat equation with a sublinear reaction term in the case when it is controlled by a static degenerate spatially averaged actuator of type ( 1.29 ). We will show that, if the actuator at hand ensures the approximate controllability of the truncated linear equation in L 2(0, 1), then the original semilinear equation is exactly controllable in any finite-dimensional subspace spanned by the eigenfunctions of the associated linear spectral problem. We will also suggest a topology in which this semilinear heat equation is globally approximately controllable at any positive time. Extensions to the case of several spatial dimensions are also discussed.

Date: 2017
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-60414-5_5

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DOI: 10.1007/978-3-319-60414-5_5

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