The talk On a generalization of the Darcy-Forchheimer equation, by Josef Žabenský, will be held on Monday April 28, 2014 at 8:30 in room K4. After that, Tomáš Gergelits will talk about his research interests with a presentation entitled Summary of papers concerning stability of Krylov subspaces. Finally, PhD students Marek Čapek and Vojtěch Kulvait will do a short progress report of the actual status of their research.
Abstract of the talk
We study mathematical properties of steady flows described by the system of equations generalizing the classical porous media models of Darcy's and Forchheimer's. The considered generalizations are outlined by implicit relations between the drag force and the velocity, that are in addition parametrized by the pressure. We analyze such drag force--velocity relations which are described through a maximal monotone graph varying continuously with the pressure. Large-data existence of a solution to this system is established, whereupon we show that under certain assumptions on data, the pressure satisfies a maximum or minimum principle, even if the drag coefficient depends on the pressure exponentially.