FAU - AvH, Erlangen, Germany; Deusto Foundation, Bilbao, Basque Country, Spain; Universidasd Autónoma de Madrid, Spain
We analyze the dynamics, numerics and control of reaction-diffusion models arising in social and biological sciences. Frequently, in applications, their control plays an important role when avoiding population extinction or propagation of infectious diseases, enhancing multicultural features, etc. When addressing these issues one of the main challenges is that the solution, typically a proportion or a density function, needs to preserve given lower and upper bounds (taking values in [0; 1])). Controlling the system to the desired final configuration then becomes complex, and sometimes even impossible.
In the present work, we analyse the controllability to constant steady-states under constraints and provide both positive results in long time horizons and exhibit also some barrier effects that may arise when the domains where the dynamics evolves is too large. For this to be done we combine the stability properties of the systems and the connectivity of the set of steady states. We will also present some numerical experiments showing the complexity of the optimal controlled dynamics.
This lecture is inspired on joint works with I. Mazari, C. Pouchol, D. Ruiz-Ballet, E. Trélat and Y. Zhu.
Enrique Zuazua (Eibar, Basque Country – Spain, 1961), Chair in Applied Analysis of the Friedrich–Alexander University Erlangen–Nürnberg (FAU) in Germany, he holds an Alexander von Humboldt Professorship.
He also leads the European Research Council Advanced Grant “DYCON: Dynamic Control”, in cooperation with the Chair of Computational Mathematics at Deusto Foundation, Bilbao (Basque Country-Spain), and the Department of Mathematics of the “Universidad Autónoma de Madrid – UAM”.
His fields of expertise in the area of Applied Mathematics cover topics related with Partial Differential Equations, Systems Control, Numerical Analysis and Data Sciences.
He has been awarded the Euskadi (Basque Country) Prize for Science and Technology 2006 and the Spanish National Julio Rey Pastor Prize 2007 in Mathematics and Information and Communication Technology and the Advanced Grants of the European research Council (ERC) NUMERIWAVES in 2010 and DYCON in 2016.
He is an Honorary member of the of Academia Europaea and Jakiunde, the Basque Academy of Sciences, Letters and Humanities, Doctor Honoris Causa from the “Université de Lorraine” in France and Ambassador of the Friedrisch-Alexandre University in Erlangen-Nurenberg, Germany.
He was also an Invited Speaker at the 2006 International Congress of Mathematicians.