ArticleArchive for rational mechanics and analysis2020
Exponential Time Decay of Solutions to Reaction-Cross-Diffusion Systems of Maxwell-Stefan Type.
Article in Archive for rational mechanics and analysis, 2020. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 1 paper.
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1 citing paper in PubMed.
- Delayed blow-up and enhanced diffusion by transport noise for systems of reaction-diffusion equations.Stochastic partial differential equations : analysis and computations · 2024Article
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Abstract
The large-time asymptotics of weak solutions to Maxwell-Stefan diffusion systems for chemically reacting fluids with different molar masses and reversible reactions are investigated. The diffusion matrix of the system is generally neither symmetric nor positive definite, but the equations admit a formal gradient-flow structure which provides entropy (free energy) estimates. The main result is the exponential decay to the unique equilibrium with a rate that is constructive up to a finite-dimensional inequality. The key elements of the proof are the existence of a unique detailed-balance equilibrium and the derivation of an inequality relating the entropy and the entropy production. The main difficulty comes from the fact that the reactions are represented by molar fractions while the conservation laws hold for the concentrations. The idea is to enlarge the space of
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