Masterclass in Applied Nonlinear PDEs
Abstract
This talk presents selected topics in science and engineering from an applied-mathematics point of view. The described natural, socioeconomic, and engineering phenomena are modeled by partial differential equations that relate state variables such as mass, velocity, and energy to their spatial and temporal variations. Typically, these equations are highly nonlinear; in many cases, they are systems and represent challenges even for the most modern and sophisticated mathematical and numerical-analytic techniques. The selected topics include flows of fluids and gases, granular-material flows, biological processes such as pattern formation on animal skins, the kinetics of rarified gases, free boundaries, semiconductor devices, and socioeconomic processes.
Brief Biography
Peter Markowich earned an M.S., a Ph.D., and the Habilitation for Applied and Numerical Mathematics at the Vienna University of Technology (TU-Wien), Austria. He became a Full Professor at the Technical University of Berlin (TUB) in 1989. From 1999 until 2007, he worked at the University of Vienna, Austria, as a Professor of Applied Analysis and from 2007-2011at the University of Cambridge, UK, as a Professor of Applied Mathematics. Since 2011 he has been a Distinguished Professor at KAUST. Professor Markowich received several awards and recognition in the course of his career. He was given the Wittgenstein Award by the Austrian Science Fund in 2000, the KAUST Inaugural Investigator Award in 2008, and the Humboldt Research Award in 2009; he was invited to give Distinguished and Excellence Lectures in scientific institutions all over the world, and he was an invited speaker at the two most important Congresses in mathematics (plenary at ICIAM in 2003 and invited at the ICM 2010). Moreover, in 2015 and again in 2018, he held a J.T.Oden Faculty Fellowship at ICES (University of Texas), the Von Neumann Visiting Professorship at the Technical University Munich in 2013, the Excellence Chair at Jiaotong University, Shanghai, in 2012, and the Excellence Chair of the Foundation Sciences Mathématiques de Paris, France in 2011. Peter Markowich is a Foreign Member of the Austrian Academy of Sciences.