Workshop on Pattern Formation and Functional Morphology, Mon, 07 Jan, 2008
Speaker: Willi Jäger
Abstract
The lecture covers a short introduction on the relevant biological processes, a survey on existing mathematical models and a report on a effective model system, derived by W. Jäger, A. Mikelic and M. Neuss-Radu 2006/07. This model is including biomechanics. Modeling flow, transport and reactions of substances in membranes and tissues and their interactions with mechanics of the solid structures on a cellular level lead to a coupled system nonlinear partial differential equations in complex geometric structures. Taking into account biological information from experiments characteristic scales are identified. The arising non-standard model systems is solved and estimates of the solutions are derived, controlling their dependence on the scale parameter. In order to derive effective equations the limit with respect to the characteristic scale parameter has to be performed. Coupling information on the processes in the micro-scale with macroscopic properties we provide theoretical answers to questions posed by physiologists studying experimentally the transport through tissues and cell layers.
URL: www.ricam.oeaw.ac.at/specsem/ssqbm/participants/abstracts/index.php
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