Tunneling estimates and approximate controllability for hypoelliptic equations

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 controllabilit...

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Bibliographic Details
Main Authors: Laurent, Camille, Léautaud, Matthieu
Format: eBook Book
Language:English
Published: Providence, Rhode Island American Mathematical Society 2022
Edition:1
Series:Memoirs of the American Mathematical Society
Subjects:
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
eigenfunctions
heat equation
control theory
hypoelliptic operators
Stability estimates
wave equation
ISBN:1470451387, 9781470451387
ISSN:0065-9266, 1947-6221
Online Access:Get full text
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Summary: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).
Bibliography:Includes bibliographical references (p. 91-95)
March 2022, volume 276, number 1357 (fifth of 7 numbers)
ISBN:1470451387
9781470451387
ISSN:0065-9266
1947-6221
DOI:10.1090/memo/1357