Local controllability to stationary trajectories of a Burgers equation with nonlocal viscosity

This article studies the local controllability to trajectories of a Burgers equation with nonlocal viscosity. By linearization we are led to an equation with a non local term whose controllability properties are analyzed by using Fourier decomposition and biorthogonal techniques. Once the existence...

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Bibliographic Details
Published inJournal of Differential Equations Vol. 264; no. 5; pp. 3664 - 3703
Main Authors Micu, Sorin, Takahashi, Takéo
Format Journal Article
LanguageEnglish
Published Elsevier Inc 01.03.2018
Subjects
Biorthogonal
Controllability to trajectories
Observability
Series of exponentials
Viscous Burgers equation
93B07
Series of exponentials
Controllability to trajectories
Biorthogonal
93B05
35Q53
35P20
93C20
Viscous Burgers equation
Observability
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Summary:This article studies the local controllability to trajectories of a Burgers equation with nonlocal viscosity. By linearization we are led to an equation with a non local term whose controllability properties are analyzed by using Fourier decomposition and biorthogonal techniques. Once the existence of controls is proved and the dependence of their norms with respect to the time is established for the linearized model, a fixed point method allows us to deduce the result for the nonlinear initial problem.
ISSN:0022-0396
1090-2732
DOI:10.1016/j.jde.2017.11.029