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 reaction-diffusion-advection equation v(tau) + h(v)v(x) = (D(v)v(x))(x) + 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 even if integral(1)(0) G(u)D(u)du > 0, unlike what happens to the mere reaction-diffusion dynamic occurring when h equivalent to 0.