论文信息 - Annihilation dynamics in the KPP-Fisher equation

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.

Masayasu Mimura | Marianito R. Rodrigo | M. Mimura | M. Rodrigo

[1] F. B. Livingstone. The wave of advance of an advantageous gene: the sickle cell gene in Liberia. 1960. , 1989, Human biology.

[2] François Hamel,et al. Entire solutions of the KPP equation , 1999 .

[3] F. Rothe,et al. Convergence to pushed fronts , 1981 .

[4] H. McKean. Application of brownian motion to the equation of kolmogorov-petrovskii-piskunov , 1975 .

[5] D. Aronson,et al. Nonlinear diffusion in population genetics, combustion, and nerve pulse propagation , 1975 .

[6] M. Bramson. Convergence of solutions of the Kolmogorov equation to travelling waves , 1983 .

[7] Paul C. Fife,et al. Mathematical Aspects of Reacting and Diffusing Systems , 1979 .

[8] François Hamel,et al. Travelling Fronts and Entire Solutions¶of the Fisher-KPP Equation in ℝN , 2001 .