PDE Seminar

The asymptotic propagation speed of the Fisher-KPP equation with effective boundary condition on a road

  • Speaker: Xinfu Chen (University of Pittsburgh)

  • Time: Jul 28, 2019, 14:00-15:00

  • Location: Conference Room 415, Hui Yuan 3#

Abstract: Of concern is the Fisher-KPP equation on the xy-plane with an ”effective boundary condition”  imposed on the x-axis.  This model, recently derived by H. Li and X.F. Wang[Nonlinearity,2017], is meant to model the scenario of fast diffusion on a “road” in a large “ field”. In their paper, the asymptotic propagation speed of this model in the horizontal direction is obtained, showing that the fast diffusion on the road does enhance spreading speed in that  direction in the field.  In this paper, we study the propagation speed in all directions, showing that away from the x-axis by a certain angle (which can be explicitly calculated in terms of parameters), the fast diffusion on the road increases propagation speed, with the speed getting larger when the direction is closer to the x-axis.  We also obtain the asymptotic spreading shape for the model with different approaches.  These results are parallel to the ones obtained by Berestycki et.al [CMP, 2016] for a different model which is meant to model the same physical phenomenon.
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