Front Propagation in Heterogeneous Media
SIAM Review, 42 (2):
161-230 (2000)DOI: 10.1137/S0036144599364296
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 trav-
eling 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.