Evolutionary Γ-convergence of gradient systems modeling slow and fast chemical reactions
Abstract
We investigate the limit passage for a system of slow and fast chemical reactions of mass-action type, where the rates of fast reactions tend to infinity. We give an elementary proof of convergence to a reduced dynamical system on the manifold of fast reaction equilibria. Then we study the entropic gradient structure of these systems and prove an E-convergence result via Γ-convergence of the primary and dual dissipation potentials, which shows that this structure carries over to the fast reaction limit in a thermodynamically consistent way. We recover the limit dynamics as a gradient flow of the entropy with respect to a pseudo-metric.
- Publication:
-
Nonlinearity
- Pub Date:
- August 2018
- DOI:
- 10.1088/1361-6544/aac353
- Bibcode:
- 2018Nonli..31.3689D