Semilinear Parabolic Equations: Mobile Point Controls Versus Locally Distributed Ones

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

Chapter Chapter 7 in Mobile Point Sensors and Actuators in the Controllability Theory of Partial Differential Equations, 2017, pp 97-120 from Springer

Abstract: Abstract In this chapter we show that, for a rather general class of 1-D semilinear parabolic equations with Lipschitz nonlinear terms, the degenerate mobile point controls can provide the same controllability results as the nondegenerate locally distributed ones. To ensure this, one needs at most two point controls that move along trajectories satisfying certain explicit differential inequalities. We also discuss some extensions of the main results to the superlinear terms and to the case of several dimensions.

Date: 2017
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-60414-5_7

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DOI: 10.1007/978-3-319-60414-5_7

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