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An application of a conjecture due to Ervedoza and Zuazua concerning the observability of the heat equation in small time to a conjecture due to Coron and Guerrero concerning the uniform controllability of a convection-diffusion equation in the vanishing viscosity limit

By Pierre Lissy

Abstract

International audienceThe aim of this short paper is to explore a new connection between a conjecture concerning sharp boundary observability estimates for the $1$-D heat equation in small time and a conjecture concerning the cost of null-controllability for a $1$-D convection-diffusion equation with constant coefficients controlled on the boundary in the vanishing viscosity limit, in the spirit of what is done in [Pierre Lissy, A link between the cost of fast controls for the $1$-D heat equation and the uniform controllability of a 1-D transport-diffusion equation, C. R. Math. Acad. Sci. Paris, Volume 352, 2012]. We notably establish that the first conjecture implies the second one as soon as the speed of the transport part is non-negative in the transport-diffusion equation

Topics: Vanishing viscosity limit, Transport-diffusion equation, Null controllability, Vanishing viscosity limit., [ MATH.MATH-OC ] Mathematics [math]/Optimization and Control [math.OC]
Publisher: Elsevier
Year: 2014
DOI identifier: 10.1016/j.sysconle.2014.04.011
OAI identifier: oai:HAL:hal-00873835v1
Provided by: Hal-Diderot

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