论文标题
随机汉堡方程的粘性冲击解决方案
Viscous shock solutions to the stochastic Burgers equation
论文作者
论文摘要
我们定义了连接同一方程式的“顶部”和“底部”的随机汉堡方程的粘性冲击溶液的概念。这种冲击通常会在太空中传播，但我们表明他们在自己的参考框架中观看时承认时不变的措施。在这样的度量下，粘性冲击是底部和顶部解决方案以及冲击位置的确定性功能。但是，必须倾斜底部和顶部解决方案的度量，以解释参考框架的更改。随着时间的流逝，我们还向最初连接两个常数的解决方案显示了这些固定的冲击解决方案的收敛结果，因为时间流向无穷大。
We define a notion of a viscous shock solution of the stochastic Burgers equation that connects "top" and "bottom" spatially stationary solutions of the same equation. Such shocks generally travel in space, but we show that they admit time-invariant measures when viewed in their own reference frames. Under such a measure, the viscous shock is a deterministic function of the bottom and top solutions and the shock location. However, the measure of the bottom and top solutions must be tilted to account for the change of reference frame. We also show a convergence result to these stationary shock solutions from solutions initially connecting two constants, as time goes to infinity.
