Travelling fronts for multidimensional nonlinear transport equations (Q1591446)

The author considers a nonlinear transport equation as a hyperbolic generalization of the well-known reaction-diffusion equation. 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 is considered. In the first case, there is a whole interval of possible speeds containing its strictly positive minimum. For subtangential nonlinearities an explicit expression for the minimal wave speed is given.