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Controllability of the Semilinear Reaction–Diffusion Equation with a Degenerate Actuator

In: Mobile Point Sensors and Actuators in the Controllability Theory of Partial Differential Equations

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  • Alexander Y. Khapalov

    (Washington State University, Department of Mathematics and Statistics)

Abstract

In this chapter we extend the discussion initiated in Chap. 4 on the controllability of semilinear parabolic PDEs to the case of the 1-D semilinear reaction-diffusion equation, assuming that it is again equipped with the static spatially averaged control of type ( 1.29 ). We will prove several results on the approximate controllability of this equation by linking them to the regularity and structure of the nonlinear term (which can also be superlinear). The obtained results are well posed in terms of the “actual steering” of the system at hand, even if it admits multiple (i.e., nonunique) solutions.

Suggested Citation

  • Alexander Y. Khapalov, 2017. "Controllability of the Semilinear Reaction–Diffusion Equation with a Degenerate Actuator," Springer Books, in: Mobile Point Sensors and Actuators in the Controllability Theory of Partial Differential Equations, chapter 0, pages 77-95, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-60414-5_6
    DOI: 10.1007/978-3-319-60414-5_6
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