Annihilation dynamics in the KPP-Fisher equation
We study the annihilation dynamics arising in the KPP-Fisher equation, proposed by Fisher in 1936 to model the propagation of a mutant gene and subsequently studied rigorously in the seminal work of Kolmogorov, Petrovskii and Piskunov. The approach is via a comparison theorem, where the comparison functions satisfy equations which are linearizable to the heat equation. In some sense, we have obtained a `linearization' of the KPP-Fisher equation.
Rodrigo, M. & Mimura, M. (2002). Annihilation dynamics in the KPP-Fisher equation. European Journal of Applied Mathematics, 13 195-204.