A well-balanced numerical scheme for a one dimensional quasilinear hyperbolic model of chemotaxis

@inproceedings{Natalini2012AWN,
  title={A well-balanced numerical scheme for a one dimensional quasilinear hyperbolic model of chemotaxis},
  author={Roberto Natalini and Magali Ribot and Monika Twarogowska},
  year={2012}
}
We introduce a numerical scheme to approximate a quasi-linear 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 handles properly the presence of vacuum and, besides, 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… CONTINUE READING

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References

Publications referenced by this paper.
Showing 1-10 of 27 references

Approximation of Hyperbolic Models for Chemosensitive Movement

SIAM J. Scientific Computing • 2005
View 6 Excerpts
Highly Influenced

Nonlinear stability of finite volume methods for hyperbolic conservation laws, and well-balanced schemes for sources

François Bouchut
Frontiers in Mathematics. Birkhauser, • 2004
View 4 Excerpts
Highly Influenced

Asymptotic-preserving and well-balanced schemes for the 1D Cattaneo model of chemotaxis movement in both hyperbolic and diffusive regimes

Laurent Gosse
J. Math. Anal. Appl., • 2012
View 1 Excerpt

Well-posedness of 1-D compressible Euler-Poisson equations with physical vacuum

Xumin Gu, Zhen Lei
J. Differential Equations, • 2012
View 1 Excerpt

Analysis and Numerical Approximations of Hydrodynamical Models of Biological Movements

Cristiana Di Russo
PhD thesis, University of Rome • 2011
View 1 Excerpt

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