We propose a new continuum model for a random genetic drift problem by employing a dynamical boundary condition approach. The new model can be viewed as a regularized Kimura equation, which admits a continuous solution and recovers the original system in the limits. The existence and uniqueness of the strong solution of the regularized system are shown. Finally, we present some numerical results for the regularized model, which indicates that the model can capture the main features of the original model.

翻译：我们通过采用动态边界条件方法，针对随机遗传漂变问题提出一种新的连续模型。该模型可视为正则化的Kimura方程，它允许连续解存在，并在极限条件下恢复原始系统。我们证明了正则化系统强解的存在唯一性。最后，我们给出了正则化模型的数值结果，表明该模型能够捕捉原始模型的主要特征。