Large time behavior of interface solutions to the heat equation with Fisher-Wright white noise
Large time behavior of interface solutions to the heat equation with Fisher-Wright white noise
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DOI：
10.1007/bf01192463
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发表时间：
1995-09
影响因子：
2
通讯作者：
R. Tribe
中科院分区：
文献类型：
--
作者：
R. Tribe
研究了由Fisher-Wright白噪声驱动的一维热传导方程。从具有紧凑支撑体的初始条件开始，解保留这种紧凑支撑体，并在有限时间内消失。在有限区域内，存在从值1变为值0的界面解。在重标度条件下，界面位置的运动接近布朗运动。具有有限个界面的解被近似为一个零化布朗运动系统。
The one-dimensional heat equation driven by Fisher-Wright white noise is studied. From initial conditions with compact support, solutions retain this compact support and die out in finite time. There exist interface solutions which change from the value 1 to the value 0 in a finite region. The motion of the interface location is shown to approach that of a Brownian motion under rescaling. Solutions with a finite number of interfaces are approximated by a system of annihilating Brownian motions.