Propagating Terraces and the Dynamics of Front-Like Solutions of Reaction-Diffusion Equations on $mathbb {R}$

The author considers semilinear parabolic equations of the form $u_t=u_xx f(u),quad xin mathbb R,t>0,$ where $f$ a $C^1$ function. Assuming that $0$ and $gamma >0$ are constant steady states, the author investigates the large-time behavior of the front-like solutions.