In recent decades, kinetic theory - originally developed as a field of mathematical physics - has emerged as one of the most prominent fields of modern mathematics. In recent years, there has been an explosion of applications of kinetic theory to other areas of research, such as biology and social sciences. This book collects lecture notes and recent advances in the field of kinetic theory of lecturers and speakers of the School Trails in Kinetic Theory: Foundational Aspects and Numerical Methods, hosted at Hausdorff Institute for Mathematics (HIM) of Bonn, Germany, 2019, during the Junior Trimester Program Kinetic Theory. Focusing on fundamental questions in both theoretical and numerical aspects, it also presents a broad view of related problems in socioeconomic sciences, pedestrian dynamics and traffic flow management.

Compact presentation of rigorous results on kinetic equations Up-to-date overview on current research on kinetic equations Broad application to related fields such as traffic management, and pedestrian dynamics

Autorentext

Giacomo Albi is Tenure Track Assistant Professor of Numerical Analysis at the Department of Computer Science, University of Verona. He received his PhD from the University of Ferrara. He was recipient of the 2014 Copernico award and the UMI-INdAM-SIMAI 2017 prize. He worked at TU Munich on the project "High Dimensional Sparse Optimal Control". In 2019 he obtained a fellowship from the HIM Bonn. His research focuses on kinetic equations, hyperbolic balance laws and control of multi-agent systems.Sara Merino-Aceituno completed a PhD in mathematics in 2015 at the University of Cambridge. She then did a post-doc at Imperial College London and got a lectureship position at the University of Sussex. Since October 2018 she is Assistant Professor at the Faculty of Mathematics of the University of Vienna. She leads a research group on applications of kinetic theory to biology, funded with a Vienna Research Group grant by the Vienna Science and Technology Fund.

Alessia Nota is Tenure Track Assistant Professor in Probability at the University of L'Aquila (DISIM). Previously she has been Postdoctoral Researcher at the University of Bonn and at the University of Helsinki. She has been member of the SFB project "The Mathematics of Emergent Effects" funded by the DFG and of the Cluster of Excellence Hausdorff Center for Mathematics. Her research area is non-equilibrium statistical mechanics with a focus on the kinetic theory of gases and plasmas.

Mattia Zanella is Tenure Track Assistant Professor in Mathematical Physics at the University of Pavia, previously he worked at the Politecnico di Torino. After completing a PhD in mathematics in 2017 at the University of Ferrara, he received the Copernico award in 2018 and the Anile Prize in 2019. In 2019 he got a fellowship from the Hausdorff Research Institute for Mathematics. His research interests are focused on uncertainty quantification, optimal control and kinetic models for collective phenomena.

Inhalt

J. A. Carrillo et al., Recent Development In Kinetic Theory Of Granular Materials: Analysis And Numerical Methods.- R. Borsche and A. Klar, Asymptotic methods for kinetic and hyperbolic evolution equations on networks.- Marina A. Ferreira, Coagulation equations for aerosol dynamics.- F. Bourdin and B. Maury, Multibody and macroscopic impact laws: a Convex Analysis Standpoint.- L. Pareschi, An introduction to uncertainty quantification for kinetic equations and related problems.- M. Pulvirenti and S. Simonella , A brief introduction to the scaling limits and effective equations in kinetic theory.- G. Toscani, Statistical description of human addiction phenomena.- A. Tosin and M. Zanella, Boltzmann-type description with cutoff of Follow-the-Leader traffic models.