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Problèmes de réaction-diffusion avec convection : Une étude mathématique et numérique.

Abstract : We study mathematically and numerically reaction-diffusion problems with convection. In the first part we prove that under some conditions the reaction-diffusion-convection operators are proper and have the Fredholm property, and we construct a topological degree for these operators. We use the degree to study bifurcations and prove the existence of traveling waves of reaction-diffusion with natural convection. We also study convective instabilities for these solutions. In the second part we investigate the influence of interfacial tension on the stability of fronts. In the case of immiscible liquids we prove that the interaction of the chemical reaction and interfacial tension may lead to a new type of instability. In the case of miscible liquids we model the transient surface tension by an additional stress in the Navier-Stokes equations. We show that the corresponding mathematical problem has a unique solution, and we observe numerically that the concentration gradients may induce convective flows. We simulate the evolution of a miscible drop under the influence of these flows: it behaves like an immiscible drop under the action of surface tension, with a tendency to get circular, or to break into droplets. We also show numerically that the tension may amplify small perturbations of plane fronts.
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https://tel.archives-ouvertes.fr/tel-00002038
Contributor : Rozenn Texier-Picard <>
Submitted on : Wednesday, November 27, 2002 - 2:44:52 PM
Last modification on : Wednesday, November 25, 2020 - 11:14:02 AM
Long-term archiving on: : Tuesday, September 11, 2012 - 6:45:22 PM

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  • HAL Id : tel-00002038, version 1

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Rozenn Texier-Picard. Problèmes de réaction-diffusion avec convection : Une étude mathématique et numérique.. Mathématiques [math]. Université Claude Bernard - Lyon I, 2002. Français. ⟨tel-00002038⟩

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