The front dynamics in reaction–diffusion equations with a piecewise linear reaction term is studied. A transition from pushed-to-pulled fronts when they propagate into the unstable state is found using a variational principle. This transition occurs for a critical value of the discontinuity...

The speed of pulled fronts for parabolic fractional-reaction-dispersal equations is derived and analyzed. From the continuous-time random walk theory we derive these equations by considering long-tailed distributions for waiting times and dispersal distances. For both cases we obtain the...

The effect of the delay time on the speed of wave fronts for interacting–diffusing models is studied analytically and numerically, both for predator–prey and competition models. It is shown that the interaction parameters may be evaluated from the time during which both species coexist until...