Elliptic and Parabolic Equations - Abstract

Postnikov, Eugene B.

Modeling 3D spatial chemical reactor: A case study in glycolitic oscillations, waves, and patterns

We present the 3D mathematical model of glycolysis reaction in an open reactor based on the modified Selkov equations: the terms coresponding to the subtrate influx and product outflow are excluded from the PDE and placed into boundary conditions. This reaction-diffusion model does not provide temporal self-sustained oscillations via reaction terms but the desired conditions could be achived by the usage of proper boundary conditions for systems with a finite thickness, i.e. the formation of oscillations, traveling waves and Turing patterns is considered as a significant volume-based effect for the appropriate parabolic PDE.
It is shown that the coresponding simulation reproduces a large variety of pattern detected in experiments taking into account a finite reactor size.
Common work with D.V. Verveyko, A.Yu.Verisokin, A.I Lavrova.