Travelling fronts for multidimensional nonlinear transport equations

We consider a nonlinear transport equation as a hyperbolic generalisation of the well-known reaction diffusion equation. We show the existence of strictly monotone travelling fronts for the three main types of the nonlinearity: the positive source term, the combustion law, and the bistable case.

In the first case there is a whole interval of possible speeds containing its strictly positive minimum. For subtangential nonlinearities we give an explicit expression for the minimal wave speed.