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A WELL-BALANCED NUMERICAL SCHEME FOR A ONE DIMENSIONAL QUASILINEAR HYPERBOLIC MODEL OF CHEMOTAXIS (Articolo in rivista)

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A WELL-BALANCED NUMERICAL SCHEME FOR A ONE DIMENSIONAL QUASILINEAR HYPERBOLIC MODEL OF CHEMOTAXIS (Articolo in rivista) (literal)

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Natalini, R; Ribot, M ; Twarogowska, M (2014)
A WELL-BALANCED NUMERICAL SCHEME FOR A ONE DIMENSIONAL QUASILINEAR HYPERBOLIC MODEL OF CHEMOTAXIS
in Communications in mathematical sciences; INT PRESS BOSTON, SOMERVILLE, MA 02143 (Stati Uniti d'America)
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CNR, Ist Applicazioni Calcolo Mauro Picone; Univ Nice Sophia Antipolis, UMR CNRS 6621, Lab JA Dieudonne; INRIA Sophia Antipolis, Project Team COFFEE, Sophia Antipolis, France (literal)

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A WELL-BALANCED NUMERICAL SCHEME FOR A ONE DIMENSIONAL QUASILINEAR HYPERBOLIC MODEL OF CHEMOTAXIS (literal)

Abstract

We introduce a numerical scheme to approximate a quasilinear hyperbolic system which models the movement of cells under the influence of chemotaxis. Since we expect to find solutions which contain vacuum parts, we propose an upwinding scheme which properly handles the presence of vacuum and which gives a good approximation of the time asymptotic states of the system. For this scheme we prove some basic analytical properties and study its stability near some of the steady states of the system. Finally, we present some numerical simulations which show the dependence of the asymptotic behavior of the solutions upon the parameters of the system. (literal)

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