WIAS Preprint No. 2227, (2016)

On the evolutionary Gamma-convergence of gradient systems modeling slow and fast chemical reactions



Authors

  • Disser, Karoline
  • Liero, Matthias
    ORCID: 0000-0002-0963-2915
  • Zinsl, Jonathan

2010 Mathematics Subject Classification

  • 34E15 49J40 49J45 80A30 92E20

Keywords

  • Gradient systems, mass-action law, dissipation potential, energy dissipation balance, multiscale evolution problems, reversible reaction kinetics, Gamma-convergence

Abstract

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.

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