Modeling Phenomena from Nature by Hyperbolic Partial Differential Equations

Kinetic-transport models that relate the intra-cellular reaction with the run-and-tumble process are considered as the correct description of microscopic level bacterial movement. Various macroscopic equations of Keller-Segel type or hyperbolic type have been derived from the pathway based kinetic-transport equations for E.coli chemotaxis. Most biological processes have a lot of noise, intrinsic or extrinsic. For E.coli chemotaxis, noise can occurs in the signaling pathways and affects the tumbling rate. We work on an individual-based model and a kinetic equation whose pathways and tumbling kernels are biologically relevant. Super diffusion can arise in the macroscopic limits, under proper scaling and conditions on the tumbling frequency as well as the form of noise. Biologically relevant pathways and tumbling kernels are considered that allows for numerical or possible experimental verifications. https://video.uni-wuerzburg.de/iframe/?securecode=d5558e90b1768ff23632cae3 9:50 am break 12 noon Jackwirth, Jonas (Würzburg): Title: A spectral method for solving the Korteweg-de-Vries equations Abstract: This is part of my Master thesis under the supervision of Christian Klingenberg. https://mfo-de.zoom.us/rec/share/yGrc4AkBH9CYt3bdDMx0SQ6DBZ0nxWTzqngihdbW3PNElmSwL9lWnIBBp4ILgPm._zUZCsGYijpcsvNj?startTime=1618308029000 4:00 pm Baumann, Lena (Würzburg): Titel: Damping phenomena for the Vlasov-Poisson-BGK equation with small collision frequencies with a focus on Landau damping Abstract: When Landau damping was discovered for the Vlasov-Poisson equation in the 1940s in a strictly mathematical way by the Soviet physicist Lev Landau this was a quite astonishing result for the mathematical and physicist community. Following the approach used by Landau we show that there is also a damping effect for the Vlasov-Poisson-BGK equation for small collision frequencies. In a first step we follow a paper by Wood and Ninham and show by analytical means and approximations that the damping effect can be split up into a collisional damping due to the BGK relaxation and a Landau damping part. In a second step we confirm this result by numerical examples. I acknowledge helpful discussions with Christian Klingenberg, Marlies Pirner & Sandra Warnecke. https://video.uni-wuerzburg.de/iframe/?securecode=cd10a9f650d094c93b3770cc