We prove the existence of a sticky-reflected solution to the heat equation on the space 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, in this case, the solution obeys the ordinary stochastic heat equation, except the points where it reaches zero. The solution has no noise at zero and a drift pushes it to stay positive. The proof is based on a new approach that can also be applied to some other types of SPDEs with discontinuous coefficients.

中文翻译：

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色噪声驱动的粘滞反射随机热方程

我们证明粘性反射溶液到热方程上的空间间隔[0的存在， 1]通过噪声有色驱动。该过程可以解释为实线上的粘性反射布朗运动的无穷大模拟，但是在这种情况下，该解决方案服从普通的随机热方程，除了达到零的点。该解决方案在零时没有噪声，并且漂移会使其保持正值。该证明基于一种新方法，该方法也可以应用于具有不连续系数的某些其他类型的SPDE。