  We consider a reaction-diffusion equation with a convection term in one space
variable, where the diffusion changes sign from the positive to the negative
and the reaction term is bistable. We study the existence of wavefront
solutions, their uniqueness and regularity. The presence of convection reveals
several new features of wavefronts: according to the mutual positions of the
diffusivity and reaction, profiles can occur either for a single value of the
speed or for a bounded interval of such values; uniqueness (up to shifts) is
lost; moreover, plateaus of arbitrary length can appear; profiles can be
singular where the diffusion vanishes.
