Constrained evolution for a quasilinear parabolic equation
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.
Cite
@article{arxiv.1602.07237,
title = {Constrained evolution for a quasilinear parabolic equation},
author = {Pierluigi Colli and Gianni Gilardi and Jürgen Sprekels},
journal= {arXiv preprint arXiv:1602.07237},
year = {2016}
}
Comments
Key words: feedback control, quasilinear parabolic equation, monotone nonlinearities, convex sets