The evolution of travelling waves in the weakly hyperbolic Fisher model

In this paper we consider an initial boundary-value problem for a weakly hyperbolic generalized Fisher equation of order p > 0. We show that for each p > 0 the large time structure of the solution involves the evolution of a propagating wavefront. However, we demonstrate that the case p = 1 is a bifurcation point in the sense that for p greater than or equal to 1 the wavefront is of reaction-diffusion type, while for 0 <p <1, then the wavefront is of reaction-relaxation type.