IDEAS home Printed from https://ideas.repec.org/h/spr/sprchp/978-3-319-60414-5_5.html
   My bibliography  Save this book chapter

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

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

Author

Listed:
  • Alexander Y. Khapalov

    (Washington State University, Department of Mathematics and Statistics)

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.

Suggested Citation

  • Alexander Y. Khapalov, 2017. "Controllability of the Semilinear Heat Equation with a Sublinear Term and a Degenerate Actuator," Springer Books, in: Mobile Point Sensors and Actuators in the Controllability Theory of Partial Differential Equations, chapter 0, pages 63-76, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-60414-5_5
    DOI: 10.1007/978-3-319-60414-5_5
    as

    Download full text from publisher

    To our knowledge, this item is not available for download. To find whether it is available, there are three options:
    1. Check below whether another version of this item is available online.
    2. Check on the provider's web page whether it is in fact available.
    3. Perform a
    for a similarly titled item that would be available.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:sprchp:978-3-319-60414-5_5. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.