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Analysis of some heterogeneous catalysis models with fast sorption and fast surface chemistry

Augner, Björn ; Bothe, Dieter (2024)
Analysis of some heterogeneous catalysis models with fast sorption and fast surface chemistry.
In: Journal of Evolution Equations, 2021, 21 (3)
doi: 10.26083/tuprints-00023426
Article, Secondary publication, Publisher's Version

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Abstract

We investigate limit models resulting from a dimensional analysis of quite general heterogeneous catalysismodels with fast sorption (i.e. exchange of mass between the bulk phase and the catalytic surface of a reactor) and fast surface chemistry for a prototypical chemical reactor. For the resulting reaction–diffusion systems with linear boundary conditions on the normalmass fluxes, but at the same time nonlinear boundary conditions on the concentrations itself, we provide analytic properties such as local-in-time well-posedness, positivity, a priori bounds and comment on steps towards global existence of strong solutions in the class W(^1,2)_p (J × Ω;R^N ), and of classical solutions in the Hölder class C(^1+α,2+2α)(J × Ω;R^N ). Exploiting that the model is based on thermodynamic principles, we further show a priori bounds related to mass conservation and the entropy principle.

Item Type: Article
Erschienen: 2024
Creators: Augner, Björn ; Bothe, Dieter
Type of entry: Secondary publication
Title: Analysis of some heterogeneous catalysis models with fast sorption and fast surface chemistry
Language: English
Date: 3 September 2024
Place of Publication: Darmstadt
Year of primary publication: 2021
Place of primary publication: Basel
Publisher: Springer International Publishing
Journal or Publication Title: Journal of Evolution Equations
Volume of the journal: 21
Issue Number: 3
DOI: 10.26083/tuprints-00023426
URL / URN: https://tuprints.ulb.tu-darmstadt.de/23426
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Origin: Secondary publication DeepGreen
Abstract:

We investigate limit models resulting from a dimensional analysis of quite general heterogeneous catalysismodels with fast sorption (i.e. exchange of mass between the bulk phase and the catalytic surface of a reactor) and fast surface chemistry for a prototypical chemical reactor. For the resulting reaction–diffusion systems with linear boundary conditions on the normalmass fluxes, but at the same time nonlinear boundary conditions on the concentrations itself, we provide analytic properties such as local-in-time well-posedness, positivity, a priori bounds and comment on steps towards global existence of strong solutions in the class W(^1,2)_p (J × Ω;R^N ), and of classical solutions in the Hölder class C(^1+α,2+2α)(J × Ω;R^N ). Exploiting that the model is based on thermodynamic principles, we further show a priori bounds related to mass conservation and the entropy principle.

Uncontrolled Keywords: Heterogeneous catalysis, Dimension analysis, Reaction diffusion systems, Surface chemistry, Surface diffusion, Sorption, Semilinear PDE, Lp-maximal, Positivity, Blow-up
Status: Publisher's Version
URN: urn:nbn:de:tuda-tuprints-234260
Classification DDC: 500 Science and mathematics > 510 Mathematics
500 Science and mathematics > 530 Physics
500 Science and mathematics > 540 Chemistry
Divisions: 04 Department of Mathematics
04 Department of Mathematics > Analysis
04 Department of Mathematics > Analysis > Mathematical Modeling and Analysis
Date Deposited: 03 Sep 2024 13:45
Last Modified: 05 Sep 2024 07:35
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