Kinetic and Related Macroscopic Models for Chemotaxis on Networks

ISBN-13: 9783745099799 / Angielski / Miękka / 2017 / 128 str.

Thi Ngoc Ha Pham

Opis

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.

O autorze

Pham, Thi Ngoc Ha2013-2017 Doktorand, Fachbereich Mathematik, TU Kaiserslautern2011-2012 Master of computational mathematics, Fachbereich Mathematik,Universitat Jaume I, Spanien2010-2011 Master of applied mathematics, Mathematik-Labor MAPMO,Université d'Orléans, Frankreich2006-2010 Bachelor in Mathematik, Cantho University, Vietnam2003-2006 Huynh Man Dat High School für die Begabten, Kiengiang, Vietnam1999-2003 Le Quy Don Mittelschule, spezielles Programm für begabte Schüler,Kiengiang, Vietnam1994-1999 Grundschule