Kinetic and Related Macroscopic Models for Chemotaxis on Networks

This thesis considers kinetic and associated macroscopic models for chemotaxis on networks.

This thesis considers kinetic and associated macroscopic models for chemotaxis on networks. By scaling and then applying moment-closure methods (including linear and nonlinear full- and half-moment methods) to the kinetic equations, we obtain full- and half-moment macroscopic models for chemotaxis as well as their drift-diffusion limit (Keller-Segel equations). Coupling conditions at the internal nodes of the network for the kinetic equations are presented and used to derive coupling conditions for the macroscopic approximations. The results of the different models are compared and relations to a Keller-Segel model on networks are discussed. For numerical approximations of the governing equations, asymptotic preserving schemes and central schemes are extended to directed graphs. Kinetic and macroscopic equations are investigated numerically and their solutions are compared for linear, tripod and more general networks.

Autorentext
2013-2017 Doktorand, Fachbereich Mathematik, TU Kaiserslautern 2011-2012 Master of computational mathematics, Fachbereich Mathematik, Universitat Jaume I, Spanien 2010-2011 Master of applied mathematics, Mathematik-Labor MAPMO, Université d'Orléans, Frankreich 2006-2010 Bachelor in Mathematik, Cantho University, Vietnam 2003-2006 Huynh Man Dat High School für die Begabten, Kiengiang, Vietnam 1999-2003 Le Quy Don Mittelschule, spezielles Programm für begabte Schüler, Kiengiang, Vietnam 1994-1999 Grundschule