Dissipation in Parabolic SPDEs
Dissipation in Parabolic SPDEs
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DOI：
10.1007/s10955-020-02540-0
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发表时间：
2018-08
影响因子：
1.6
通讯作者：
D. Khoshnevisan;Kunwoo Kim;C. Mueller;Shang-Yuan Shiu
中科院分区：
文献类型：
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作者：
D. Khoshnevisan;Kunwoo Kim;C. Mueller;Shang-Yuan Shiu
抛物型Anderson问题的间歇性研究通常集中在解的矩上，它可以描述概率空间中的高峰。本文在有限空间区间上建立了方程，并研究了间歇性的另一部分，即解接近于零的概率空间部分。这个集合的概率非常接近于1，我们证明了在这个集合上，解在空间上的最大值接近于0。因此，我们发现几乎可以肯定的是，随着时间的增加，解的空间极值以指数速度趋于零。我们还表明，如果噪声项非常大，那么解的上零点非常小的集合的概率就非常高。
The study of intermittency for the parabolic Anderson problem usually focuses on the moments of the solution which can describe the high peaks in the probability space. In this paper we set up the equation on a finite spatial interval, and study the other part of intermittency, i.e., the part of the probability space on which the solution is close to zero. This set has probability very close to one, and we show that on this set, the supremum of the solution over space is close to 0. As a consequence, we find that almost surely the spatial supremum of the solution tends to zero exponentially fast as time increases. We also show that if the noise term is very large, then the probability of the set on which the supremum of the solution is very small has a very high probability.