Traveling Waves of a Kinetic Transport Model for the KPP-Fisher Equation

@article{Cuesta2012TravelingWO,
  title={Traveling Waves of a Kinetic Transport Model for the KPP-Fisher Equation},
  author={Carlota M. Cuesta and Sabine Hittmeir and Christian Schmeiser},
  journal={SIAM J. Math. Analysis},
  year={2012},
  volume={44},
  pages={4128-4146}
}
A reactive kinetic transport equation whose macroscopic limit is the KPP-Fisher equation is considered. In a scale, where collisions occur at a faster rate than reactions, existence of traveling waves close to those of the KPP-Fisher equation is shown. The method adapts a micro-macro decomposition in the spirit of the work of Caflisch and Nicolaenko for the Boltzmann equation. Stability of these waves is shown for perturbations in a weighted L2-space, where the weight function is exponential… CONTINUE READING