Evolution Equations Long Time Behavior and Control London Mathematical Society Lecture Note Series

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.

Preface Kaïs Ammari and Stéphane Gerbi; 1. Controllability of parabolic systems – the moment method Farid Ammar Khodja; 2. Stabilization of semilinear PDEs, and uniform decay under discretization Emmanuel Trélat; 3. A null controllability result for the linear system of Thermoelastic plates with a single control Carlos Castro and Luz de Teresa; 4. Doubly connected V-states for the generalized surface Quasi-Geostrophic equations Francisco de la Hoz, Zineb Hassainia and Taoufik Hmidi; 5. About least-squares type approach to address direct and controllability problems Arnaud Münch and Pablo Pedregal; 6. A note on the asymptotic stability of wave-type equations with switching time-delay Serge Nicaise and Cristina Pignotti; 7. Ill-posedness of coupled systems with delay Lisa Fischer and Reinhard Racke; 8. Controllability of parabolic equations by the flatness approach Philippe Martin, Lionel Rosier and Pierre Rouchon; 9. Mixing for the burgers equation driven by a localised two-dimensional stochastic forcing Armen Shirikyan.

Kaïs Ammari is professor of mathematics at the Université de Monastir, Tunisia. His domain of expertise includes analysis of partial differential equations, control theory and operator semigroup theory. He has held visiting professorships at various universities in France, Italy and Spain, and has developed a number of international cooperative projects. He is the head of the research mathematical laboratory of Analysis and Control of PDEs (ACEDP). He serves on the editorial boards of various mathematics journals.
Stéphane Gerbi is associate professor of mathematics at Université Savoie Mont Blanc, France. His area of expertise includes fluid dynamics, computational fluid dynamics, numerical analysis, scientific computing, analysis of partial differential equations and control. He has held visiting professorships at various universities in Spain (Madrid and Bilbao) and has also developed a number of international cooperative projects with researchers in Lebanon, Tunisia and Algeria.