| Issue |
ESAIM: COCV
Volume 18, Number 4, October-December 2012
|
|
|---|---|---|
| Page(s) | 1207 - 1224 | |
| DOI | https://doi.org/10.1051/cocv/2012004 | |
| Published online | 27 March 2012 | |
Controllability properties for the one-dimensional Heat equation under multiplicative or nonnegative additive controls with local mobile support∗,∗∗
1
Departamento de Matemáticas, Estadística y Computación, Avda. de
los Castros, s/n, Universidad de Cantabria, 39005
Santander,
Spain
This email address is being protected from spambots. You need JavaScript enabled to view it.
2
Department of Mathematics, Washington State
University, Pullman,
99164-3113
WA,
USA
This email address is being protected from spambots. You need JavaScript enabled to view it.
Received:
21
February
2011
Revised:
7
November
2011
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.
Mathematics Subject Classification: 35K05 / 35K20 / 93B05
Key words: Parabolic equation / approximate controllability / multiplicative controls / nonnegative locally distributed controls
The work of the first author was partially supported by the Spanish Ministry of Science and Innovation under grant MTM2008 − 04206.
The work of the second author was supported in part by the NSF Grant DMS-1007981.
© EDP Sciences, SMAI, 2012
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