Spreading in a cone for the Fisher-KPP equation

[摘要] In this paper we consider the spreading phenomena in the Fisher-KPP equation in a high dimensional cone with Dirichlet boundary condition. We show that any solution starting from a nonnegative and compact supported initial data spreads and converges to the unique positive steady state. Moreover, the asymptotic spreading speeds of the front in all directions pointing to the opening are c(0) (which is the minimal speed of the traveling wave solutions of the 1-dimensional Fisher-KPP equation). Surprisingly, they do not depend on the shape of the cone, the propagating directions and the boundary condition. (C) 2019 Elsevier Inc. All rights reserved.

[发布日期] 2019-12-05

[关键词] Fisher-KPP equation;Cone;Spreading phenomena;Steady state;Traveling wave solution