论文标题
具有两个积分约束的中性木村方程的解
Solution of the Neutral Kimura equation with two integral constraints
论文作者
论文摘要
木村方程是种群遗传学中使用的漂移扩散类型的退化部分微分方程。它的解决方案不仅要满足方程式，还满足一系列作为整体约束的保护定律。在这项工作中，我们考虑了两种类型的人群，而没有突变或选择，即所谓的中性进化。我们从Gegenbauer多项式方面获得明确的解决方案。为了满足整体限制，有必要证明Gegenbauer多项式满足的新关系。还研究了长期的渐近性。
The Kimura equation is a degenerated partial differential equation of drift-diffusion type used in population genetics. Its solution is required to satisfy not only the equation but a series of conservation laws formulated as integral constraints. In this work, we consider a population of two types evolving without mutation or selection, the so-called neutral evolution. We obtain explicit solutions in terms of Gegenbauer polynomials. To satisfy the integral constraints it is necessary to prove new relations satisfied by the Gegenbauer polynomials. The long-term in time asymptotic is also studied.
