Evolution equations: long time behavior and control

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The proceedings of the summer school held at the Université Savoie Mont Blanc, France, 'Mathematics in Savoie 2015', whose theme was long time behavior and control of evolution equations. The event was attended by world-leading researchers from the community of control theory, as well as young researchers from around the globe. This volume contains surveys of active research topics, along with original research papers containing exciting new results on the behavior of evolution equations. It wi…

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Title Statements

Full title :Evolution equations : long time behavior and control / edited by Kaïs Ammari, Stéphane Gerbi.

Summary

The proceedings of the summer school held at the Université Savoie Mont Blanc, France, 'Mathematics in Savoie 2015', whose theme was long time behavior and control of evolution equations. The event was attended by world-leading researchers from the community of control theory, as well as young researchers from around the globe. This volume contains surveys of active research topics, along with original research papers containing exciting new results on the behavior of evolution equations. It will therefore benefit both graduate students and researchers. Key topics include the recent view on the controllability of parabolic systems that permits the reader to overview the moment method for parabolic equations, as well as numerical stabilization and control of partial differential equations.

Edition Statements

Publication Date:ß2018

Publication Statements

Publisher(s):Cambridge University Press
Place of Publication:Cambridge, England
Language:eng
Publication Date:ß2018

The Physical Object

Description:1 online resource (194 pages)

Edition Identifiers

ISBN:1108331033, 9781108331036
oclc:on1013733130
LC Classification:QA377.3
Dewey Decimal:515.353

Cover -- Series Page -- Title page -- Imprints Page -- Contents -- Preface -- List of Contributors Present at the Summer School -- 1 Controllability of Parabolic Systems: The Moment Method -- 1.1 Introduction -- 1.2 Parabolic Systems and Controllability Concepts -- 1.3 Controllability Results for the Scalar Case: The Carleman Inequality -- 1.4 First Application to a Parabolic System -- 1.5 The Moment Method -- 1.5.1 Presentation: Example 1 -- 1.5.2 Generalization of the Moment Problem -- 1.5.3 Going Back to the Heat Equation

1.5.4 Example 2: A Minimal Time of Control for a 2 x 2 Parabolic System due to the Coupling Function 1.5.5 Example 3: A Minimal Time of Control Due to the Condensation of the Eigenvalues of the System -- 1.6 The Index of Condensation -- 1.6.1 Definition -- 1.6.2 Optimal Condensation Grouping -- 1.6.3 Interpolating Function -- 1.6.4 An Interpolating Formula of Jensen -- 1.6.5 Going Back to the Boundary Control Problem -- References -- 2 Stabilization of Semilinear PDEs, and Uniform Decay under Discretization -- 2.1 Introduction and General Results

2.1.1 General Setting2.1.2 In Finite Dimension -- 2.1.3 In Infinite Dimension -- 2.1.4 Existing Results for Discr…