WIAS Preprint No. 2232, (2016)
Constrained evolution for a quasilinear parabolic equation
- Colli, Pierluigi
- Gilardi, Gianni
- Sprekels, Jürgen
2010 Mathematics Subject Classification
- 35K59 35K20 34H05 80M50 93B52
- feedback control, quasilinear parabolic equation, monotone nonlinearities, convex sets
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.
- J. Optim. Theory Appl., 170 (2016), pp. 713--734.