Evolution of bounding functions for the solution of KPP-Fisher equation in bounded domains
The KPP-Fisher equation was proposed by R. A. Fisher as a model to describe the propagation of advantageous genes. Subsequently, it was studied rigorously by Kolmogorov, Petrovskii, and Piskunov. In this paper, we study the dynamics of the KPP-Fisher equation in bounded domains by giving bounds on its solution. The bounding functions satisfy nonlinear equations which are linearizable to the heat equation. In addition to describing the dynamics of the KPP-Fisher equation, we also recover some previous results concerning its asymptotic behavior. We perform numerical simulations to compare the solution of the Fisher equation and the bounding functions.