Travelling fronts for multidimensional nonlinear transport equations

  • Hartmut Schwetlick (Zürich)
A3 01 (Sophus-Lie room)


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.

Anne Dornfeld

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