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Controllability properties for the one-dimensional Heat equation under multiplicative or nonnegative additive controls with local mobile support∗∗∗

Published online by Cambridge University Press:  27 March 2012

Luis Alberto Fernández  and
Alexander Yuri Khapalov
Luis Alberto Fernández
Affiliation:
Departamento de Matemáticas, Estadística y Computación, Avda. de los Castros, s/n, Universidad de Cantabria, 39005 Santander, Spain. lafernandez@unican.es
Alexander Yuri Khapalov
Affiliation:
Department of Mathematics, Washington State University, Pullman, 99164-3113 WA, USA; khapala@math.wsu.edu
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Abstract

We discuss several new results on nonnegative approximate controllability for the one-dimensional Heat equation governed by either multiplicative or nonnegative additive control, acting within a proper subset of the space domain at every moment of time. Our methods allow us to link these two types of controls to some extend. The main results include approximate controllability properties both for the static and mobile control supports.

Keywords

Parabolic equationapproximate controllabilitymultiplicative controlsnonnegative locally distributed controls
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 18 , Issue 4 , October 2012 , pp. 1207 - 1224
Copyright
© EDP Sciences, SMAI, 2012

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