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A hyperbolic model of chemotaxis on a network: a numerical study

G. Bretti, R. Natalini, M. Ribot (2014)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

In this paper we deal with a semilinear hyperbolic chemotaxis model in one space dimension evolving on a network, with suitable transmission conditions at nodes. This framework is motivated by tissue-engineering scaffolds used for improving wound healing. We introduce a numerical scheme, which guarantees global mass densities conservation. Moreover our scheme is able to yield a correct approximation of the effects of the source term at equilibrium. Several numerical tests are presented to show the...

Analysis of lumped parameter models for blood flow simulations and their relation with 1D models

Vuk Milišić, Alfio Quarteroni (2004)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

This paper provides new results of consistence and convergence of the lumped parameters (ODE models) toward one-dimensional (hyperbolic or parabolic) models for blood flow. Indeed, lumped parameter models (exploiting the electric circuit analogy for the circulatory system) are shown to discretize continuous 1D models at first order in space. We derive the complete set of equations useful for the blood flow networks, new schemes for electric circuit analogy, the stability criteria that guarantee...

Analysis of lumped parameter models for blood flow simulations and their relation with 1D models

Vuk Milišić, Alfio Quarteroni (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

This paper provides new results of consistence and convergence of the lumped parameters (ODE models) toward one-dimensional (hyperbolic or parabolic) models for blood flow. Indeed, lumped parameter models (exploiting the electric circuit analogy for the circulatory system) are shown to discretize continuous 1D models at first order in space. We derive the complete set of equations useful for the blood flow networks, new schemes for electric circuit analogy, the stability criteria that...

Continuity of solutions of a quasilinear hyperbolic equation with hysteresis

Petra Kordulová (2012)

Applications of Mathematics

This paper is devoted to the investigation of quasilinear hyperbolic equations of first order with convex and nonconvex hysteresis operator. It is shown that in the nonconvex case the equation, whose nonlinearity is caused by the hysteresis term, has properties analogous to the quasilinear hyperbolic equation of first order. Hysteresis is represented by a functional describing adsorption and desorption on the particles of the substance. An existence result is achieved by using an approximation of...

Couches limites semilinéaires

Franck Sueur (2006)

Annales de la faculté des sciences de Toulouse Mathématiques

On s’intéresse à des problèmes mixtes pour des systèmes symétriques hyperboliques multidimensionnels semilinéaires perturbés par une petite viscosité. La description à la limite non visqueuse recquiert des développements du type BKW mettant en évidence une couche limite caractéristique (CLC) et une couche limite non caractéristique (CLNC). Ce thème traité dans [12] est ici enrichi de trois améliorations :l’étude inclut des développements ayant peu de termes (comme un seul terme),on étudie aussi...

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