带弹性强迫项的Burgers方程与随机过程的联系
Connection between the Burgers equation with an elastic forcing term and a stochastic process
摘要：
本文给出了带弹性强迫项$-κ^{2} x+f(t)$，$κ\in\mathbb{R}$的一维Burgers方程的完整解析解.现有的两种方法的情况下，$κ=0$适应和推广使用变量和函数变换，有效的空间和时间的所有值。该方法中福克-普朗克方程的出现允许将由Burgers方程描述的流体模型与Ornstein-Uhlenbeck过程连接起来。
英文摘要：
We present a complete analytical resolution of the one dimensional Burgers equation with the elastic forcing term $-κ^{2} x+f(t)$, $κ\in\mathbb{R}$. Two methods existing for the case $κ=0$ are adapted and generalized using variable and function transformations, valid for all values of space an time. The emergence of a Fokker-Planck equation in the method allows to connect a fluid model, depicted by the Burgers equation, with an Ornstein-Uhlenbeck process.
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