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- Title
THE ENTROPY METHOD FOR REACTION-DIFFUSION SYSTEMS WITHOUT DETAILED BALANCE: FIRST ORDER CHEMICAL REACTION NETWORKS.
- Authors
FELLNER, KLEMENS; PRAGER, WOLFANG; TANG, BAO Q.
- Abstract
In this paper, the applicability of the entropy method for the trend towards equilibrium for reaction-diffiusion systems arising from first order chemical reaction networks is studied. In particular, we present a suitable entropy structure for weakly reversible reaction networks without detail balance condition. We show by deriving an entropy-entropy dissipation estimate that for any weakly reversible network each solution trajectory converges exponentially fast to the unique positive equilibrium with computable rates. This convergence is shown to be true even in cases when the diffiusion coefficients of all but one species are zero. For non-weakly reversible networks consisting of source, transmission and target components, it is shown that species belonging to a source or transmission component decay to zero exponentially fast while species belonging to a target component converge to the corresponding positive equilibria, which are determined by the dynamics of the target component and the mass injected from other components. The results of this work, in some sense, complete the picture of trend to equilibrium for first order chemical reaction networks.
- Subjects
ENTROPY; REACTION-diffusion equations; CHEMICAL reactions; ENERGY dissipation; EQUILIBRIUM constant (Chemistry)
- Publication
Kinetic & Related Models, 2017, Vol 10, Issue 4, p1055
- ISSN
1937-5093
- Publication type
Article
- DOI
10.3934/krm.2017042