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This volume presents a timely overview of control theory and related topics, such as the reconstruction problem, the stability of PDEs, and the Calderón problem. The chapters are based on talks given at the conference "Control & Related Fields" held in Seville, Spain in March 2023. In addition to providing a snapshot of these areas, chapters also highlight breakthroughs on more specific topics, such as:
- Stabilization of an acoustic system
- The Kramers-Fokker-Planck operator
- Control of parabolic equations
- Control of the wave equation
Advances in Partial Differential Equations and Control will be a valuable resource for both established researchers as well as more junior members of the community.
List of contents
Part I: Control of partial differential equations.- Energy decay estimate for a wave-plate interface transmission problem with only two dynamical boundary controls.- Uniform stabilization of an acoustic system.- Some results on the energy decay of solutions for a wave equation with a general internal feedback of diffusive type.- Numerical approximation of the boundary control for the wave equation with periodic oscillating coefficients.- Numerical impulse controllability for parabolic equations by a penalized HUM approach.- Part II: Related fields.- Decoding the Kramers-Fokker-Planck Operator: An overview.- Exponential decay of solutions to linear evolution equations with time-dependent time delay.- Central Nervous System Action on Rolling Balance Board Robust Stabilization: Computer Algebra and MID-based feedback design.- Study of the numerical method for an inverse problem of a simplified intestinal crypt.
About the author
Kaïs Ammari is full professor of mathematics at the University of Monastir (Tunisia). He got his PhD from Ecole Polytechnique in Palaiseau (France). 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. He has developed a number of international cooperative projects. He is the director of the research Lab of Analysis and Control of PDE (ACEDP lab).
Anna Doubova is an Associate Professor in the Department of Differential Equations and Numerical Analysis at the University of Seville, Spain. She received a degree in Mechanics and Applied Mathematics from Lomonosov University (Moscow) and a PhD in Mathematics from the University of Seville. Her research relates to analysis, control and inverse problems of PDEs with applications in physics, engineering, biology and other sciences. She publishes regularly in high impact international journals.
Stéphane Gerbi is associate professor at the mathematics department of the University Savoie Mont Blanc, Chambéry, France. He got his PhD from Ecole Normale Supérieure de Lyon (France). His thesis is about a mathematical analysis of detonations in duct. His domain 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).
He has developed a number of international cooperative projects with Algerian, Lebanon, Spain and Tunisia and publishes regularly in high impact international journals.
Manuel González Burgos is Full Professor of Mathematical Analysis in the Department of Differential Equations and Numerical Analysis, Universidad de Sevilla, Spain. His fields of specialization include partial differential equations and control theory, with a particular focus on the controllability properties of scalar and non-scalar parabolic problems with controls exerted in a part of the domain or on a part of the boundary. He has published over 40 papers in peer-reviewed journals.
