Front Propagation in Heterogeneous Media

  • Authors:
  • Jack Xin

  • Affiliations:
  • -

  • Venue:
  • SIAM Review
  • Year:
  • 2000

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Abstract

A review is presented of recent results on front propagation in reaction-diffusion-advection equations in homogeneous and heterogeneous media. Formal asymptotic expansions and heuristic ideas are used to motivate the results wherever possible. The fronts include constant-speed monotone traveling fronts in homogeneous media, periodically varying traveling fronts in periodic media, and fluctuating and fractal fronts in random media. These fronts arise in a wide range of applications such as chemical kinetics, combustion, biology, transport in porous media, and industrial deposition processes. Open problems are briefly discussed along the way.