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A time-optimal boundary controllability problem for the heat equation in a ball

Published online by Cambridge University Press:  01 December 2014

Sorin Micu  and
Laurenţiu Emanuel Temereancă
Sorin Micu
Affiliation:
Facultatea de Matematica si Stiinte ale Naturii, Universitatea din Craiova, 13 AI Cuza Street, 200585 Craiova, Romania, (sd_micu@yahoo.com; temereanca_laurentiu@yahoo.com)
Laurenţiu Emanuel Temereancă
Affiliation:
Facultatea de Matematica si Stiinte ale Naturii, Universitatea din Craiova, 13 AI Cuza Street, 200585 Craiova, Romania, (sd_micu@yahoo.com; temereanca_laurentiu@yahoo.com)
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Abstract

The aim of this paper is to study a boundary time-optimal control problem for the heat equation in a two-dimensional ball. The main ingredient is the extension of a result concerning Müntz polynomials due to Borwein and Erdélyi that allows us to prove an observability inequality for the dynamical system's truncation to a finite number of modes. This result, combined with a well-known Lebeau–Robbiano argument used to show the null-controllability of parabolic type equations, enables us to deduce the existence, uniqueness and bang-bang properties for the boundary time-optimal control.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 144 , Issue 6 , December 2014 , pp. 1171 - 1189
Copyright
Copyright © Royal Society of Edinburgh 2014 

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