WIAS Preprint No. 2232, (2016)

Constrained evolution for a quasilinear parabolic equation


Authors

  • Colli, Pierluigi
    ORCID: 0000-0002-7921-5041
  • Gilardi, Gianni
    ORCID: 0000-0002-0651-4307
  • Sprekels, Jürgen
    ORCID: 0009-0000-0618-8604

2010 Mathematics Subject Classification

  • 35K59 35K20 34H05 80M50 93B52

Keywords

  • feedback control, quasilinear parabolic equation, monotone nonlinearities, convex sets

DOI

10.20347/WIAS.PREPRINT.2232

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 K of L2(Ω). Then, we consider convex sets of obstacle or double-obstacle type, and we can act on the factor of the feedback control in order to be able to reach the convex set within a finite time, by proving rigorously this property.

Appeared in

  • J. Optim. Theory Appl., 170 (2016), pp. 713--734.

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