Hostname: page-component-6bf8c574d5-w79xw Total loading time: 0 Render date: 2025-02-15T09:28:35.094Z Has data issue: false hasContentIssue false
  • English
  • Français

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)
Get access Rights & Permissions [Opens in a new window]

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 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)