Evolution Equations: Long Time Behavior and Control

Description

This volume constitutes the proceedings of the summer school MIS 2015, “Mathematics In Savoie 2015,” whose theme was: “Evolution Equations: long time behavior and control.” This summer school was held at the University Savoie Mont Blanc, Chambéry in the period June 15–18, 2015 (see http://lama.univ-savoie.fr/ MIS2015 for details). It was organized by Kaïs Ammari, UR Analysis and Control of PDE, University of Monastir, Tunisia, and Stéphane Gerbi, Laboratoire de Mathématiques, University Savoie Mont Blanc, France. The summer school consisted of two mini-courses in the morning while the afternoons were devoted to various contributions on the theme. The 䱌rst mini-course was held by Farid Ammar-Khodja, University of Franche-Comté, France. The topic was: “Controllability of parabolic sys- tems: the moment method.” This recent point of view on the controllability of parabolic systems permits to overview the moment method for parabolic equations. This course constitutes the 䱌rst part of this volume. The second part of this volume is devoted to the second mini-course which was held by Emmanuel Trélat, UPMC, Paris. The topic was “Stabilization of semilinear PDEs, and uniform decay under discretiza- tion.” This course was devoted to the numerical stabilization and control of partial differential equations and more speci䱌cally it addresses the prob- lem of the construction of numerical feedback control that will preserve the theoretical rate of decay. Contents......Page 5 Preface......Page 8 List of Contributors......Page 9 1 Controllability of Parabolic Systems: The Moment Method......Page 12 2 Stabilization of Semilinear PDEs, and Uniform Decay under Discretization......Page 42 3 A Null-Controllability Result for the Linear System of Thermoelastic Plates with a Single Control......Page 88 4 Doubly Connected V-States for the Generalized Surface Quasi-geostrophic Equations......Page 101 5 About Least-Squares Type Approach to Address Direct and Controllability Problems......Page 129 6 A Note on the Asymptotic Stability of Wave-Type Equations with Switching Time-Delay......Page 148 7 Ill-Posedness of Coupled Systems with Delay......Page 162 8 Controllability of Parabolic Equations by the Flatness Approach......Page 172 9 Mixing for the Burgers Equation Driven by a Localized Two-Dimensional Stochastic Forcing......Page 190