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 operators

Research 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.

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 operators

Research 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.