有色噪声驱动的粘性反射随机Heat Equation
Sticky-Reflected Stochastic Heat Equation Driven by Colored Noise
摘要：
证明了在色噪声驱动下，热方程在空间区间$[0,1]$上粘性反射解的存在性。这个过程可以被解释为一个无限维的模拟粘性反射布朗运动在实数线上，但现在的解决方案服从通常的随机热方程，除了点，它达到零。在零的解决方案没有噪音和漂移推动它保持积极的。证明是基于一种新的方法，也可以适用于其他类型的SPDE与不连续系数。
英文摘要：
We prove the existence of a sticky-reflected solution to the heat equation on the spatial interval $[0,1]$ driven by colored noise. The process can be interpreted as an infinite-dimensional analog of the sticky-reflected Brownian motion on the real line, but now the solution obeys the usual stochastic heat equation except points where it reaches zero. At zero the solution has no noise and a drift pushes it to stay positive. The proof is based on a new approach that can also be applied to other types of SPDEs with discontinuous coefficients.
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