Existence of Traveling Waves for the Generalized F-KPP Equation

被引:4
|
作者
Kollar, Richard [1 ]
Novak, Sebastian [2 ]
机构
[1] Comenius Univ, Dept Appl Math & Stat, Bratislava 84248, Slovakia
[2] IST Austria, Campus 1, A-3400 Klosterneuburg, Austria
基金
欧洲研究理事会;
关键词
Traveling waves; Fisher equation; KPP equation; LINEAR DETERMINACY; PISCOUNOV EQUATION; FRONT PROPAGATION; DIFFUSION; DYNAMICS; PATTERNS; ADVANCE; SPEED;
D O I
10.1007/s11538-016-0244-3
中图分类号
Q [生物科学];
学科分类号
07 ; 0710 ; 09 ;
摘要
Variation in genotypes may be responsible for differences in dispersal rates, directional biases, and growth rates of individuals. These traits may favor certain genotypes and enhance their spatiotemporal spreading into areas occupied by the less advantageous genotypes. We study how these factors influence the speed of spreading in the case of two competing genotypes under the assumption that spatial variation of the total population is small compared to the spatial variation of the frequencies of the genotypes in the population. In that case, the dynamics of the frequency of one of the genotypes is approximately described by a generalized Fisher-Kolmogorov-Petrovskii-Piskunov (F-KPP) equation. This generalized F-KPP equation with (nonlinear) frequency-dependent diffusion and advection terms admits traveling wave solutions that characterize the invasion of the dominant genotype. Our existence results generalize the classical theory for traveling waves for the F-KPP with constant coefficients. Moreover, in the particular case of the quadratic (monostable) nonlinear growth-decay rate in the generalized F-KPP we study in detail the influence of the variance in diffusion and mean displacement rates of the two genotypes on the minimal wave propagation speed.
引用
收藏
页码:525 / 559
页数:35
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