FRONT PROPAGATION IN BISTABLE REACTION-DIFFUSION-ADVECTION EQUATIONS

The paper deals with the existence and properties of front propagation between the stationary states 0 and 1 of the reactiondiffusion- advection equation v_τ + h(v)v_x = D(v)v_xx + G(v), where G is a bistable reaction term and D is 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.