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Compact Seminar

SWS 2+2: Mathematische Modellierung mit Partiellen Differentialgleichungen

Block; Zeit nach Vereinbarung, Vorbesprechung: Do, 18.10.2012, 14.00, INF 294, SR 214

Organisers: Anna Marciniak-Czochra, Piotr Gwiazda, Alexandra Köthe

Abstract: Partial differential equations have long served to model nonlinear reactions and transport processes in complex systems. In the last years, there has been a fast development of PDE methods dictated by the novel aspects of biological observation. This seminar will be devoted to mathematical techniques used to formulate and analyze model equations of mathematical biology (methods of partial differential equations, dynamical systems, asymptotic analysis and measure theory). The goal is to highlight novel mathematical problems arising in such modeling. Main topics will be: discrete and continuous structured population dynamics, pattern formation, chemotaxis and haptotaxis. Recent results and theoretical methods will be discussed in the context of biological applications. The analytical level of presentations and corresponding literature may be adjusted to the profile of participating students; nevertheless the Analysis 3 level is required.

Program

Monday 28.01

Agnieszka Ulikowska: "Stuctured population models in metric spaces" (Abstract)

Jędrzej Jabłoński: "Optimal foraging in the case of planktivorous fish" (Abstract)

Tuesday 29.01

Alexandra Köthe: "Solution two-point boundary problems by phase plane analysis" (Abstract)

Steffen Härting: "Stability analysis of discontinuous steady states of a system consisting of one ODE and one reaction diffusion equation" (Abstract)

Wednesday 30.01

Mareike Janßen: "Modeling tissue compressibility and growth to investigate mechanical pattern formation" (Abstract)

Moritz Mercker: "Chemical versus mechano-chemical pattern formation during embryogenesis" (Abstract)