Reaction-Diffusion systems: front propagation and spatial structures

Abstract

After the pioneering works of Kolmogorov, Petrovskii and Piskunov [1] and Fisher [2] in 1937 on the nonlinear diffusion equation and its traveling wave solutions, scientists from many different disciplines have been captivated by questions about structure, formation and dynamics of patterns in reactive media. Combustion, spreading of epidemics, diffusive transport of chemicals in cells and population dynamics are just a few examples bearing witness of the influence of those works in different areas of modern science.