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. (C) 2000 Editions scientifiques et medicales Elsevier SAS.