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Doubova, Anna and Fernández Cara, E. and González Burgos, Manuel and Zuazua Iriondo, Enrique
(2002)
*On the Controllability of Parabolic Systems with a Nonlinear Term Involving the State and the Gradient.*
SIAM Journal on Control and Optimization, 41
(3).
pp. 798-819.
ISSN 0363-0129

PDF
262kB |

Official URL: http://epubs.siam.org/sicon/resource/1/sjcodc/v41/i3/p798_s1

## Abstract

We present some results concerning the controllability of a quasi-linear parabolic equation (with linear principal part) in a bounded domain of ${\mathbb R}^N$ with Dirichlet boundary conditions. We analyze the controllability problem with distributed controls (supported on a small open subset) and boundary controls (supported on a small part of the boundary). We prove that the system is null and approximately controllable at any time if the nonlinear term $f( y, \nabla y)$ grows slower than $|y| \log^{3/2}(1+ |y| + |\nabla y|) + |\nabla y| \log^{1/2}(1+ |y| + |\nabla y|)$ at infinity (generally, in this case, in the absence of control, blow-up occurs). The proofs use global Carleman estimates, parabolic regularity, and the fixed point method.

Item Type: | Article |
---|---|

Uncontrolled Keywords: | Controllability, Parabolic equations, Nonlinear gradient terms |

Subjects: | Sciences > Mathematics > Numerical analysis |

ID Code: | 12178 |

Deposited On: | 07 Feb 2011 08:59 |

Last Modified: | 12 Dec 2018 15:07 |

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