Singular convergence of nonlinear hyperbolic chemotaxis systems to Keller-Segel type models

DOI10.3934/dcdsb.2010.13.79zbMath1186.35011arXiv0807.3852OpenAlexW2061139036MaRDI QIDQ2654521

Marco Di Francesco, Donatella Donatelli

Publication date: 19 January 2010

Published in: Discrete and Continuous Dynamical Systems. Series B (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0807.3852

zbMATH Keywords

chemotaxiscompensated compactnessnonlinear diffusiondiffusive relaxationdiffusive limitvolume filling effect

Mathematics Subject Classification ID

Singular perturbations in context of PDEs (35B25) Initial-boundary value problems for first-order hyperbolic systems (35L50) Cell movement (chemotaxis, etc.) (92C17)

Related Items (12)

Asymptotic Stability of Diffusion Waves of a Quasi-Linear Hyperbolic-Parabolic Model for Vasculogenesis ⋮ The Hyperbolic-Parabolic Chemotaxis System for Vasculogenesis: Global Dynamics and Relaxation Limit Toward a Keller–Segel Model ⋮ Convergence to nonlinear diffusion waves for solutions of hyperbolic-parabolic chemotaxis system ⋮ Large time behavior of a hyperbolic-parabolic model of vasculogenesis ⋮ Global existence and weak-strong uniqueness for chemotaxis compressible Navier-Stokes equations modeling vascular network formation ⋮ Fully discrete convergence analysis of non-linear hyperbolic equations based on finite element analysis ⋮ A survey on well-balanced and asymptotic preserving schemes for hyperbolic models for chemotaxis ⋮ Asymptotic-preserving and well-balanced schemes for the 1D Cattaneo model of chemotaxis movement in both hyperbolic and diffusive regimes ⋮ Vanishing dielectric constant regime for the Navier Stokes Maxwell equations ⋮ Convergence to nonlinear diffusion waves for a hyperbolic-parabolic chemotaxis system modelling vasculogenesis ⋮ Stability of rarefaction wave for viscous vasculogenesis model ⋮ A numerical comparison between degenerate parabolic and quasilinear hyperbolic models of cell movements under chemotaxis

Uses Software

• Chemotaxis

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