Viscous Shock Solutions to the Stochastic Burgers Equation
Viscous Shock Solutions to the Stochastic Burgers Equation
复制标题
随机 Burgers 方程的粘性冲击解
DOI：
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发表时间：
2020
影响因子：
2.5
通讯作者：
L. Ryzhik
中科院分区：
文献类型：
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作者：
Alexander Dunlap;L. Ryzhik
我们定义了一个概念的粘性冲击解的随机Burgers方程，连接“顶部”和“底部”空间静止的解决方案相同的方程。这样的冲击一般在空间中旅行，但我们表明，他们承认时不变的措施时，在自己的参考系。在这样的测量下，粘性激波是底部和顶部解以及激波位置的确定性函数。然而，底解和顶解的测量必须倾斜以考虑参考系的变化。我们还显示了收敛的结果，这些固定的冲击解决方案，最初连接两个常数的解决方案，随着时间的推移到无穷大。
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.
影响因子：
2
作者：
Ivan Corwin;A. Hammond
通讯作者：
Ivan Corwin;A. Hammond