Approximate controllability of the viscous Burgers equation on the real line

The paper is devoted to studying the 1D viscous Burgers equation controlled by an external force. It is assumed that the initial state is essentially bounded, with no decay condition at infinity, and the control is a trigonometric polynomial of low degree with respect to the space variable. We const...

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Bibliographic Details
Published inarXiv.org
Main Author Shirikyan, Armen
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 30.12.2013
Subjects
Burgers equation
Controllability
Linear equations
Polynomials
Stability
Topology
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Summary:The paper is devoted to studying the 1D viscous Burgers equation controlled by an external force. It is assumed that the initial state is essentially bounded, with no decay condition at infinity, and the control is a trigonometric polynomial of low degree with respect to the space variable. We construct explicitly a control space of dimension 11 that enables one to steer the system to any neighbourhood of a given final state in local topologies. The proof of this result is based on an adaptation of the Agrachev-Sarychev approach to the case of an unbounded domain.
ISSN:2331-8422