I discuss three very different forward PDE problems which need data assimilation/inverse approaches to make them potentially useful in practical applications. The first problem is a reaction-diffusion system for biological transportation network formation and adaptation, the second is a highly nonstandard parabolic free boundary problem describing price formation in economic markets and the third problem is the incompressible Navier-Stokes-Forchheimer-Brinkmann system for flow in porous media.
 

Professor Peter A. Markowich is currently a Distinguished Professor at the Computer Science, Electrical and Mathematical Sciences and Engineering Division, King Abdullah University of Science and Technology (KAUST); a Professor at the Department of Applied Mathematics and Theoretical Physics (DAMTP), University of Cambridge; and a professor of the Faculty of Mathematics, University of Vienna. He got his PhD from TU Vienna in 1980 and defended his ‘Habilitation’ for Applied and Numerical Mathematics at TU Vienna in 1984. His research interests are focused on Applied Partial Differential Equations (PDE) including Analysis, Numerics and Modeling as well as their applications in physics, biology, engineering and socio-economics. In fact, he is one of the world leaders in applied PDEs and their applications as well as scientific and engineering computing. He has published over 150 scientific papers and 5 books. He has been awarded many prestigious awards including the Wittgenstein Award by the Austrian Science Fund in 2000, the Royal Society Wolfson Research Merit Award in 2007, the Humboldt Research Award in 2009, etc. He has been invited to give plenary/invited talks in numerous international conferences including a Plenary Lecture at the 5th International Congress on Industrial and Applied Mathematics in 2003, an Invited Lecture at the International Congress of Mathematicians in 2010, etc. Last but not the least, he has trained many PhD students who have become famous mathematicians in the mean-time.