Constrained evolution for a quasilinear parabolic equation

2016/02/23 by Pierluigi Colli, Colli, Pierluigi, Gianni Gilardi +3
Mathematics · #34H05 #35K20 #35K59 #80M50 #93B52 #Analysis of PDEs (math.AP) #FOS: Mathematics #Optimization and Control (math.OC) #math.AP #math.OC #msc:34H05 #msc:35K20 #msc:35K59 #msc:80M50 #msc:93B52

paper · pdf · doi:10.48550/arxiv.1602.07237

Key words: feedback control, quasilinear parabolic equation, monotone nonlinearities, convex sets

arxiv created 2016/06/16 · arxiv updated 2016/06/17

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.

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