BEGIN:VCALENDAR METHOD:PUBLISH PRODID:en-www-math-fau-de//Events//EN VERSION:2.0 BEGIN:VEVENT SUMMARY:Kolloquium: Michael Herty (Universität RWTH Aachen): Uncertai nty Quantification for Nonlinear Hyperbolic Differential Equations UID:8974acb1-8512-4355-94f9-7fad3b0b4c66 DESCRIPTION:Uncertainty Quantification for Nonlinear Hyperbolic Differ ential Equations –\; Vortragender: Michael Herty\, Universität R WTH Aachen –\; Einladender: M. Gugat We are interested in quantif ying uncertainties that appear in nonlinear hyperbolic partial differe ntial equations arising in a variety of applications from fluid flow t o traffic modeling. A common approach to treat the stochastic componen ts of the solution is by using generalized polynomial chaos expansions . This method was successfully applied in particular for general ellip tic and parabolic PDEsas well as linear hyperbolic stochastic equation s. More recently\, gPC methods have been successfully applied to parti cular hyperbolic PDEs using the explicit form of nonlinearity or the p articularity of the studied system structure as\, e.g.\, in the p-syst em. While such models arise in many applications\, e.g.\, in atmospher ic flows\, fluid flows under uncertain gas compositions and shallow wa ter flows\, a general gPC theory with corresponding numerical methods are still at large. Typical analytical and numerical challenges that a ppear for the gPC expanded systems are loss of hyperbolicity and posit ivity of solutions (like gas density or water depth). Any of those eff ects might trigger severe instabilities within classical finite-volume or discontinuous Galerkin methods. We will discuss properties and con ditions to guarantee stability and present numerical results on select ed examples. DTSTART:20230718T143000Z DTEND:20230718T153000Z LOCATION:HS H13\, Cauerstr. 11\, Erlangen DTSTAMP:20260725T070809Z END:VEVENT END:VCALENDAR