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Seminar

SWS 2: Mathematics of Pattern Formation

Time and place: Tuesdays, 14.15-15.45 in BIOQUANT, SR 043 if not specified differently

Organizational meeting/Vorbesprechung/Themenvergabe: Tuesday, October 15, 14.15-15.45 SR 041

Organizers: Prof. Dr. Anna Marciniak-Czochra and Dipl.Math. Steffen Härting

Abstract: Classical mathematical models of biological or chemical pattern formation have been developed using partial differential equations of reaction-diffusion type. The seminar will be devoted to mathematical analysis of such equations, in particularly different mechanisms of pattern formation. The topics of the seminar will include a classical theory for existence, uniqueness and regularity of solutions of reaction-diffusion equations and mathematical methods for the analysis of model dynamics, such as theory of invariant rectangles and comparison principle. We will focus on two-component reaction-diffusion and reaction-diffusion-ode systems which serve as a basic models to understand pattern formation mechanisms. The seminar will cover a classical theory of Turing-type pattern formation (based diffusion-driven instability of spatially homogenous steady states), and more recent approaches such as models based on the existence of multiple steady states and hysteresis. Analysis of pattern formation involves analysis of two-point boundary value problems, solving spectral problems and applying of singular perturbation methods. Therefore, it is expected that the participants of the seminar have basic knowledge in partial differential equations and functional analysis.