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Tunneling estimates and approximate controllability for hypoelliptic equations

by Laurent, Camille , Léautaud, Matthieu

in Differential equations, Hypoelliptic / Partial differential equations -- Close-to-elliptic equations and systems -- Hypoelliptic equations. msc / Partial differential equations -- Hyperbolic equations and systems -- Wave equation. msc / Partial differential equations -- Parabolic equations and systems -- Heat equation. msc / Partial differential equations -- Qualitative properties of solutions -- Continuation and prolongation of solutions. msc / Partial differential equations -- Spectral theory and eigenvalue problems -- Asymptotic distribution of eigenvalues and eigenfunctions. msc / Systems theory; control -- Controllability, observability, and system structure -- Controllability. msc / Systems theory; control -- Controllability, observability, and system structure -- Observability. msc

2022

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Tunneling estimates and approximate controllability for hypoelliptic equations

by Laurent, Camille , Léautaud, Matthieu

2022

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Tunneling estimates and approximate controllability for hypoelliptic equations

by Laurent, Camille , Léautaud, Matthieu

2022

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Tunneling estimates and approximate controllability for hypoelliptic equations

Laurent, Camille,

Léautaud, Matthieu

2022

Overview

This memoir is concerned with quantitative unique continuation estimates for equations involving a “sum of squares” operator The first result is the tunneling estimate The main result is a stability estimate for solutions to the hypoelliptic wave equation We then prove the approximate controllability of the hypoelliptic heat equation We also explain how the analyticity assumption can be relaxed, and a boundary Most results turn out to be optimal on a family of Grushin-type operators. The main proof relies on the general strategy to produce quantitative unique continuation estimates, developed by the authors in Laurent-Léautaud (2019).

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Publisher

American Mathematical Society

Subject

Differential equations, Hypoelliptic

/ Partial differential equations -- Close-to-elliptic equations and systems -- Hypoelliptic equations. msc

/ Partial differential equations -- Hyperbolic equations and systems -- Wave equation. msc

/ Partial differential equations -- Parabolic equations and systems -- Heat equation. msc

/ Partial differential equations -- Qualitative properties of solutions -- Continuation and prolongation of solutions. msc

/ Partial differential equations -- Spectral theory and eigenvalue problems -- Asymptotic distribution of eigenvalues and eigenfunctions. msc

/ Systems theory; control -- Controllability, observability, and system structure -- Controllability. msc