On the evolutionary Gamma-convergence of gradient systems modeling slow and fast chemical reactions
- Disser, Karoline
- Liero, Matthias
- Zinsl, Jonathan
2010 Mathematics Subject Classification
- 34E15 49J40 49J45 80A30 92E20
- Gradient systems, mass-action law, dissipation potential, energy dissipation balance, multiscale evolution problems, reversible reaction kinetics, Gamma-convergence
We investigate the limit passage for a system of ordinary differential equations modeling slow and fast chemical reaction 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 acting in the slow reaction directions 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. We recover the limit dynamics as a gradient flow of the entropy with respect to a pseudo-metric.
- Nonlinearity, 31 (2018), pp. 3689--3706, DOI 10.1088/1361-6544/aac353 .