论文标题
在小方差的制度中，无限模型的库奇问题
The Cauchy problem for the infinitesimal model in the regime of small variance
论文作者
论文摘要
我们研究了具有性生殖方式的定量遗传学模型相关的凯奇问题解决方案的渐近行为。它结合了特征依赖性死亡率和非线性积分繁殖操作符“无限模型”和描述后代和平均父母性状之间的标准偏差的参数。我们表明，在对死亡率m的轻度假设下，当偏差很小时，解决方案保持接近具有较小差异的高斯轮廓，及时均匀。而且，我们准确地表征了人口中平均特征的动力学。我们的研究扩展了有关模型固定溶液的存在和独特性的先前结果。它依靠扰动分析技术以及对校正的尖锐描述，以测量与高斯剖面的偏离。
We study the asymptotic behavior of solutions of the Cauchy problem associated to a quantitative genetics model with a sexual mode of reproduction. It combines trait-dependent mortality and a nonlinear integral reproduction operator "the infinitesimal model" with a parameter describing the standard deviation between the offspring and the mean parental traits. We show that under mild assumptions upon the mortality rate m, when the deviations are small, the solutions stay close to a Gaussian profile with small variance, uniformly in time. Moreover we characterize accurately the dynamics of the mean trait in the population. Our study extends previous results on the existence and uniqueness of stationary solutions for the model. It relies on perturbative analysis techniques together with a sharp description of the correction measuring the departure from the Gaussian profile.
