Nonmonotone chemotactic invasion: high-resolution simulations, phase plane analysis and new benchmark problems

DOI10.1016/J.JCP.2007.03.016zbMath1201.92024OpenAlexW2153457957MaRDI QIDQ996479

Matthew J. Simpson, Kerry A. Landman

Publication date: 14 September 2007

Published in: Journal of Computational Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jcp.2007.03.016

zbMATH Keywords

chemotaxisshockshigh-resolution methodsinvasionhyperbolic conservation law

Mathematics Subject Classification ID

PDEs in connection with biology, chemistry and other natural sciences (35Q92) Cell movement (chemotaxis, etc.) (92C17)

Related Items (6)

A Bayesian sequential learning framework to parameterise continuum models of melanoma invasion into human skin ⋮ Travelling waves for a velocity-jump model of cell migration and proliferation ⋮ The PAC-MAN model: benchmark case for linear acoustics in computational physics ⋮ Travelling wave solutions in a negative nonlinear diffusion-reaction model ⋮ Tactically-driven nonmonotone travelling waves ⋮ A fourth-order central Runge-Kutta scheme for hyperbolic conservation laws

Cites Work

• Tactically-driven nonmonotone travelling waves
• A survey of several finite difference methods for systems of nonlinear hyperbolic conservation laws
• A two parameter family of travelling waves with a singular barrier arising from the modelling of extracellular matrix mediated cellular invasion
• New high-resolution central schemes for nonlinear conservation laws and convection-diffusion equations
• Chemotactic and diffusive migration on a nonuniformly growing domain: numerical algorithm development and applications
• Solidification of a binary alloy: finite-element, single-domain simulation and new benchmark solutions
• Finite Volume Methods for Hyperbolic Problems
• High‐Resolution Finite Volume Methods for Dusty Gas Jets and Plumes
• Diffusive and Chemotactic Cellular Migration: Smooth and Discontinuous Traveling Wave Solutions
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