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Seminar

Mathematical Theory of Pattern Formation

Time and Place:
Preliminary talk (Vorbesprechung): Tuesday, October 13, 2015, 2 pm, INF 294, SR 214

Abstract:
Spatial and spatio-temporal structures occur widely in physics, chemistry and biology. In many cases, they seem to be generated spontaneously. Understanding the evolution of spatial patterns and the mechanisms which create them are among the crucial issues of developmental biology. 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 particular different mechanisms of pattern formation. The topics will include the classical theory of Turing-type pattern formation (based on 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. We will focus on two-component reaction-diffusion and reaction-diffusion-ode systems which serve as basic models to understand pattern formation mechanisms. Mathematical theory will be illustrated on examples of models from developmental biology The seminar content will range from basic topics related to mathematical modeling and ordinary differential equations to analysis of reaction-diffusion equations (evolution equations, two-point boundary value problems and spectral problems). The analytical level of presentations and corresponding literature may be adjusted to the profile of participating students; nevertheless the Analysis 3 level is required.