Propagation of Fronts in 1D

This lecture covers the propagation of fronts in 1D systems using a mechanical analogy, focusing on bistable systems and the Kolmogorov-Fisher equation. The slides illustrate the concept of bistability, different cases of wave propagation, and the mechanical analogy for the problem f(u) = u(1-u)(u-a). The instructor discusses the existence of fronts in spatial systems, the different cases of propagation velocities, and the quartic potential. The lecture also delves into the Kolmogorov-Fisher equation, the cubic case, and the prediction capabilities of the mechanical analogy. Furthermore, the slides touch upon the concept of heteroclinic orbits and the spatial coordination of the Xenopus cell cycle.