标题： 广义FKPP方程的行波解的存在性 显示英文标题

标题： Existence of traveling waves for the generalized FKPP equation

摘要： 基因型的差异可能是个体扩散率、方向偏差和生长率差异的原因。 这些特征可能有利于某些基因型，并促进它们在占据较少优势基因型区域的空间-时间扩散。 我们研究了这些因素在两种竞争基因型情况下的传播速度影响，并表明在保持空间均匀总种群假设下，其中一个基因型的频率动态近似由广义的Fisher-Kolmogorov-Petrovskii-Piskunov (FKPP)方程描述。 这个带有(非线性)频率依赖扩散和对流项的广义FKPP方程允许行波解(前沿/梯度)，这些解表征了优势基因型的入侵。 我们的存在结果推广了对于具有常系数的FKPP的经典行波理论。 此外，对于广义FKPP中的二次(单稳态)非线性增长-衰减率的特殊情况，我们详细研究了两个基因型的扩散方差和平均位移速率对最小波传播速度的影响。 显示英文摘要

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 spatio-temporal 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 and show that under the assumption of maintenance of spatially homogeneous total population the dynamics of the frequency of one of the genotypes is approximately described by the generalized Fisher-Kolmogorov-Petrovskii-Piskunov (FKPP) equation. This generalized FKPP equation with (nonlinear) frequency dependent diffusion and advection terms admits traveling wave solutions (fronts/clines) that characterize the invasion of the dominant genotype. Our existence results generalize the classical theory for traveling waves for the FKPP with constant coefficients. Moreover for the particular case of the quadratic (monostable) nonlinear growth-decay rate in the generalized FKPP we study in details the influence of the variance in diffusion and mean displacement rates of the two genotypes on the minimal wave propagation speed.