TY  - GEN
TI  - Modeling Subdiffusion Using Reaction Diffusion Systems
Y1  - 2007///
UR  - https://archiv.ub.uni-heidelberg.de/volltextserver/7168/
T3  - IWR-Preprints
AV  - public
N2  -   In many types of media, and in particular within living cells or   within their membranes, diffusing species do not follow Fick's laws,   but instead show transient subdiffusive behavior. Formulating   spatiotemporal models that take this behavior into account is a   delicate matter, as one is faced with the choice of resorting either   to fractional calculus or to microscopic descriptions. In this   article, we provide an alternative designed to be easier to tackle   analytically and numerically than the existing approaches.   Specifically, starting from the Continuous Time Random Walk model,   we construct linear reaction diffusion systems that can be used as   components within such a model, and which capture the defining   properties of subdiffusion. We show how to impose physically   relevant parameters, and prove stability and mass conservation.   While applications to cellular biology are our main motivation, our   approach is abstract, and should thus be applicable to any situation   where anomalous subdiffusion is observed. 
ID  - heidok7168
A1  - Mommer, Mario S.
A1  - Lebiedz, Dirk
ER  -