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Travelling fronts for multidimensional nonlinear transport equations

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

Abstract

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

MPI for Mathematics in the Sciences Contact via Mail

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