Serdecznie zapraszamy na cykl wykładów
prof. dr hab. Jacka Banasiaka
(Politechnika Łódzka, University of KwaZulu)
na temat: Positive semigroups with applications
Wykłady odbywać się będą w sali nr 905 (wieżowiec) w terminach: 24-26 i 28 listopada, godz. 09:15-12, 27 listopada, godz. 14:15-17.
Opis: Many problems in natural sciences require a notion of positivity: only non-negative densities, population sizes or probabilities make sense in real life. This imposes certain constrains on the the modelling process but also, coupled with the norm structure of underlying spaces, oers new and powerful tools for analyzing complex evolutionary systems. The presented lectures describe such an intertwining of topological and order structures in analysis of linear dynamical systems, mainly arising in mathematical biology and kinetic theory. In the lectures we shall discuss the ways in which the positivity impacts on classical results concerning the well-posedness and long-term behaviour of innite dimensional linear systems and also we shall show how it facilitates analysis of concrete evolutionary problems such as transport and diusion systems on networks, structured population models and fragmentation-coagulation equations.