Analysis of fronts in reaction-dispersal processes

The existence of traveling wave front solutions in reaction-dispersal processes is discussed. The minimum speed selection of pulled fronts was studied and was shown that these fronts exist only when both the Laplace transform of φ(t) and the bilateral transform of φ(x) fulfill a certain restriction. The evolution equation for the reaction-dispersal process according to the continuous-time random walk theory (CTRW) was derived. The results show that the minimum speed selection for traveling wave fronts is not always possible, so the waiting time and the dispersal distance distributions cannot be arbitrarily chosen.