Fronts in Homogeneous Media

Abstract

Front propagation and interface motion occur in many scientific areas such as chemical kinetics, combustion, biology, transport in porous media, and industrial deposition processes. In spite of these different applications, the basic phenomena can all be modeled using nonlinear partial differential equations or systems of such equations. Since the pioneering work of Kolmogorov, Petrovsky and Piskunov (KPP) [134] and Fisher [91] in 1937 on traveling fronts of the reaction-diffusion equations, the field has gone through enormous growth and development. However, studies of fronts in heterogeneous media have been more recent. Heterogeneities are always present in natural environments, such as fluid convection effects in combustion (wind factor in spreading of forest fires), inhomogeneous porous structures in transport of solutes, noise effects in biology, and deposition processes. It is both a fundamental and a practical problem to understand how heterogeneities influence the characteristics of front propagation such as front speeds, front profiles, and front locations. Our goal here is to give a tutorial of recent results on front propagation in heterogeneous (especially random) media in a coherent and motivating manner. It is not the intention of the book to give a complete survey, and so the cited references will cover only a portion of the vast literature.