Averaging principles: From a microscopic to a macroscopic point of view

16.06.2016, 14:15 Uhr  –  Campus Golm, Haus 14, Raum 0.38
Forschungsseminar Diskrete Spektraltheorie

Markus Kunze (Konstanz)

We consider diffusion problems in a domain which is further subdivided by semi-permeable membranes. Such problems frequently occur in applications in biology, for example when studying the concentration of calcium in the different parts of a life cell. One can describe the evolution of the concentration (on a microscopic level) by a PDE model involving suitable transmission conditions reflecting the behaviour of the diffusing particles at the membranes. A different (more macroscopic) approach is to merely look at the fraction of the total calcium in each part. This leads to an ODE model, involving as many equations as we have parts of the cell. We show how the solutions of the PDE model converge to the solutions of the ODE model when speeding up the diffusion while keeping the flux through the membranes constant. This is based on joint work with Adam Bobrowski and Bogdan Kazmierczak.