Constrained Evolution for a Quasilinear Parabolic Equation

Pierluigi Colli (), Gianni Gilardi () and Jürgen Sprekels ()
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Pierluigi Colli: Università di Pavia
Gianni Gilardi: Università di Pavia
Jürgen Sprekels: Humboldt-Universität zu Berlin

Journal of Optimization Theory and Applications, 2016, vol. 170, issue 3, No 1, 713-734

Abstract: 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.

Keywords: Feedback control; Quasilinear parabolic equation; Monotone nonlinearities; Convex sets; 35K59; 35K20; 34H05; 80M50; 93B52 (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1007/s10957-016-0970-6

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