On the minimal time null controllability of the heat equation

Ovidiu Cârjă; Alina Lazu

doi:10.3934/proc.2009.2009.143

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2009, Volume 2009: 143-150. Doi: 10.3934/proc.2009.2009.143 open access

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On the minimal time null controllability of the heat equation

Ovidiu Cârjă^1, and
Alina Lazu^2,

1.
Department of Mathematics, " Al. I. Cuza" University, Iaşi, 700506
2.
Department of Mathematics, "Gh. Asachi" Technical University, Iaşi, 700506

Received: May 31, 2008

Revised: April 30, 2009

Published: August 2009

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Abstract

We show that the heat equation modelled as $y'=Ay+u$ in $L^1(\Omega)$ is null controllable by controls in $L^{\infty}(0,T;L^p(\Omega))$ with $1< p<\infty$. Moreover, the corresponding minimal time function is Hölder continuous.

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Mathematics Subject Classification: Primary: 93B05, 49K15; Secondary: 34H05.

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