Traveling Shock Waves Arising in a Model of Malignant Invasion

  title={Traveling Shock Waves Arising in a Model of Malignant Invasion},
  author={A. J. Perumpanani and B. P. Marchant and John Norbury},
  journal={SIAM Journal of Applied Mathematics},
Members of a family of traveling wave solutions for a simple two-variable model of malignant invasion driven by haptotaxis are shown to have shocks (which satisfy an entropy condition) and to be computationally stable. By seeking traveling wave solutions, a PDE model, equivalent to three first order PDEs defined on the real space and time axes, may be reduced to an ordinary differential equation system, which can be studied in a two-dimensional phase plane. This phase plane is shown to contain… CONTINUE READING

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