论文标题
通过选择的布朗运动引起的一个自由边界问题
A free boundary problem arising from branching Brownian motion with selection
论文作者
论文摘要
我们研究了抛物线偏微分方程的自由边界问题，在该方程中，该解决方案通过积分约束耦合到移动边界。问题出现是作为相互作用的粒子系统的流体动力学极限，该系统涉及带有选择的布朗运动，即所谓的布朗蜜蜂模型，该模型在伴侣纸上进行了研究。在本文中，我们证明了对自由边界问题的解决方案的存在和唯一性，并且我们在较大的时间限制中表征了解决方案的行为。
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.
