This volume presents an accessible overview of mathematical control theory and analysis of PDEs, providing young researchers a snapshot of these active and rapidly developing areas. The chapters are based on two mini-courses and additional talks given at the spring school "Trends in PDEs and Related Fields" held at the University of Sidi Bel Abbès, Algeria from 8-10 April 2019. In addition to providing an in-depth summary of these two areas, chapters also highlight breakthroughs on more specific topics such as:

• Sobolev spaces and elliptic boundary value problems
• Local energy solutions of the nonlinear wave equation
• Geometric control of eigenfunctions of Schrödinger operatorsResearch in PDEs and Related Fields will be a valuable resource to graduate students and more junior members of the research community interested in control theory and analysis of PDEs.

Autorentext

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 semi-group 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).