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Constrained Evolution for a Quasilinear Parabolic Equation

Author

Listed:
  • Pierluigi Colli

    (Università di Pavia)

  • Gianni Gilardi

    (Università di Pavia)

  • Jürgen Sprekels

    (Humboldt-Universität zu Berlin
    Weierstrass Institute for Applied Analysis and Stochastics)

Abstract

In the present contribution, a feedback control law is studied for a quasilinear parabolic equation. First, we prove the well-posedness and some regularity results for the Cauchy–Neumann problem for this equation, modified by adding an extra term which is a multiple of the subdifferential of the distance function from a closed convex set of the space of square-integrable functions. Then, we consider convex sets of obstacle or double-obstacle type and prove rigorously the following property: if the factor in front of the feedback control is sufficiently large, then the solution reaches the convex set within a finite time and then moves inside it.

Suggested Citation

  • Pierluigi Colli & Gianni Gilardi & Jürgen Sprekels, 2016. "Constrained Evolution for a Quasilinear Parabolic Equation," Journal of Optimization Theory and Applications, Springer, vol. 170(3), pages 713-734, September.
    • Handle: RePEc:spr:joptap:v:170:y:2016:i:3:d:10.1007_s10957-016-0970-6
    DOI: 10.1007/s10957-016-0970-6
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    References listed on IDEAS

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    1. Pisano, Alessandro & Usai, Elio, 2011. "Sliding mode control: A survey with applications in math," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 81(5), pages 954-979.
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