Front propagation in bistable reaction-diffusion-advection equations

The paper deals with the existence and properties of frontpropagation between the stationary states 0 and 1 of the reaction-diffusion-advection equation with a bistable reaction term G and a strictly positive diffusive process. We show that the additional transport term h can cause the disappearance of such wavefronts and prove that their existence depends both on the local behavior of G and h near the unstable equilibrium and on a suitable sign condition on h in [0, 1]. We also provide an estimate of the wave speed, which can be negative unlike what happens to the mere reaction-diffusion dynamic occurring when h ≡ 0.