Displaying similar documents to “Hybrid model for the Coupling of an Asymptotic Preserving scheme with the Asymptotic Limit model: The One Dimensional Case⋆”

High-order WENO scheme for polymerization-type equations

Pierre Gabriel, Léon Matar Tine (2010)

ESAIM: Proceedings

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Polymerization of proteins is a biochemical process involved in different diseases. Mathematically, it is generally modeled by aggregation-fragmentation-type equations. In this paper we consider a general polymerization model and propose a high-order numerical scheme to investigate the behavior of the solution. An important property of the equation is the mass conservation. The WENO scheme is built to preserve the total mass of proteins ...

V. Bonnaillie-Noël, D. Brancherie, M. Dambrine, F. Hérau, S. Tordeux, G. Vial (2011)

ESAIM: Proceedings

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This paper is a survey of articles [5, 6, 8, 9, 13, 17, 18]. We are interested in the influence of small geometrical perturbations on the solution of elliptic problems. The cases of a single inclusion or several well-separated inclusions have been deeply studied. We recall here techniques to construct an asymptotic expansion. Then we consider moderately close inclusions, i.e. the distance between the inclusions tends to zero more slowly than their characteristic size. We provide a complete...

Analytical results on a model for damaging in domains and interfaces

Elena Bonetti, Michel Frémond (2011)

ESAIM: Control, Optimisation and Calculus of Variations

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This paper deals with a model describing damage processes in a (nonlinear) elastic body which is in contact with adhesion with a rigid support. On the basis of phase transitions theory, we detail the derivation of the model written in terms of a PDE system, combined with suitable initial and boundary conditions. Some internal constraints on the variables are introduced in the equations and on the boundary, to get physical consistency. We prove the existence of global in time solutions...

Diffusion models of multicomponent mixtures in the lung

L. Boudin, D. Götz, B. Grec (2010)

ESAIM: Proceedings

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In this work, we are interested in two different diffusion models for multicomponent mixtures. We numerically recover experimental results underlining the inadequacy of the usual Fick diffusion model, and the importance of using the Maxwell-Stefan model in various situations. This model nonlinearly couples the mole fractions and the fluxes of each component of the mixture. We then consider a subregion of the lower part of the lung, in...