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Behavior of Solutions of the Semilinear Heat Equation in Vanishing Time and Controllability

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

Author

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  • Alexander Y. Khapalov

    (Washington State University, Department of Mathematics and Statistics)

Abstract

In this chapter we discuss the problem of approximate controllability of the semilinear heat equation with, possibly, superlinear nonlinear terms in u and ∇u, governed by degenerate controls. Our approach focuses on the study of the asymptotic behavior in vanishing time of those solutions to the semilinear heat equation that are generated by controls solving the controllability problem at hand. The provided examples include the static distributed and time-dependent lumped controls.

Suggested Citation

  • Alexander Y. Khapalov, 2017. "Behavior of Solutions of the Semilinear Heat Equation in Vanishing Time and Controllability," Springer Books, in: Mobile Point Sensors and Actuators in the Controllability Theory of Partial Differential Equations, chapter 0, pages 41-62, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-60414-5_4
    DOI: 10.1007/978-3-319-60414-5_4
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