色噪声驱动下随机heat equation的不稳定性前沿
On the intermittency front of stochastic heat equation driven by colored noises
摘要：
研究了乘性中心高斯噪声驱动下随机热方程解的高峰值（半波阵面）在$\mathbb{R}^d$中的传播。假设噪声在时间和空间上都具有一般的齐次协方差，并且在Wick产品的意义上解释该解决方案。我们给出了一些估计的传播速度的上界和下界，基于一个时刻公式的解决方案。当空间协方差由里斯核给出时，我们给出了更精确的传播速度的界。
英文摘要：
We study the propagation of high peaks (intermittency front) of the solution to a stochastic heat equation driven by multiplicative centered Gaussian noise in $\mathbb{R}^d$. The noise is assumed to have a general homogeneous covariance in both time and space, and the solution is interpreted in the senses of the Wick product. We give some estimates for the upper and lower bounds of the propagation speed, based on a moment formula of the solution. When the space covariance is given by a Riesz kernel, we give more precise bounds for the propagation speed.
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