A free boundary problem in biological selection models

选择最适应的还是选择最幸运的：在进化中Goodhart定律的出现

Selection of the fittest or selection of the luckiest: the emergence of Goodhart's law in evolution

研究通过理想化模型展示选择压力影响适应速度，超过阈值后随机性主导，导致适应速度和基因多样性下降，体现Goodhart定律。

A free boundary problem arising from branching Brownian motion with selection

We study a free boundary problem for a parabolic partial differential equation in which the solution is coupled to the moving boundary through an integral constraint. The problem arises as the hydrodynamic limit of an interacting particle system involving branching Brownian motion with selection, the so-called Brownian bees model which is studied in a companion paper. In this paper we prove existence and uniqueness of the solution to the free boundary problem, and we characterise the behaviour of the solution in the large time limit.

On the boundary classification of $Λ$-Wright-Fisher processes with frequency-dependent selection

We construct extensions of the pure-jump $Λ$-Wright-Fisher processes with frequency-dependent selection ($Λ$-WF processes with selection) beyond their first passage time at the boundary $1$. We show that they satisfy some duality relationships with the block counting process of simple exchangeable fragmentation-coalescence processes (EFC). One-to-one correspondences between the nature of the boundary $1$ of the $Λ$-WF process with selection and the boundary $\infty$ of the block counting process are established. New properties for the $Λ$-WF processes with selection and the block counting proc…

双侧自由边界问题：源自分支-选择粒子系统的现象

Two-Sided Free Boundary Problems Arising From Branching-Selection Particle Systems

本文研究了分支-选择粒子系统，扩展了经典的N粒子分支布朗运动模型，通过参数p决定左右粒子的删除，建立自由边界问题并证明其解的存在性和正则性，同时证明了渐近速度收敛到极限自由边界问题的旅行波速度。

Stochastic Cahn-Hilliard-Navier-Stokes equations with the dynamic boundary: Martingale weak solution, Markov selection

The existence of global martingale weak solution for the 2D and 3D stochastic Cahn-Hilliard-Navier-Stokes equations driven by multiplicative noise in a smooth bounded domain is established. In particular, the system is supplied with the dynamic boundary condition which accounts for the interaction between the fluid components and the rigid walls. The proof is completed by a three-level approximate scheme combining a fixed point argument and the stochastic compactness argument, overcoming challenges from strong nonlinearity, dynamic boundary and random effect. Then, we prove the existence of an…

自由边界问题的弱形式及其在带选择的粒子系统流体动力学极限中的应用

A weak formulation of free boundary problems and its application to hydrodynamic limits of particle systems with selection

本文提出了一类抛物型自由边界问题的弱形式，并将其应用于带选择的粒子系统的流体动力学极限，证明了在经典自由边界不存在时该弱形式解的唯一性与收敛性。