The objective of this paper is to prove the existence of a global solution to a certain stochastic partial differential equation subject to the [Formula: see text]-norm being constrained. The corresponding evolution equation can be seen as the projection of the unconstrained problem onto the tangent space of the unit sphere [Formula: see text] in a Hilbert space [Formula: see text].

中文翻译：

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具有希尔伯特流形解的非线性随机热方程的全局解

本文的目的是证明某个随机偏微分方程的全局解的存在，该方程受到 [公式：见文本]-范数的约束。对应的演化方程可以看作是无约束问题在希尔伯特空间[公式：见文]中单位球体[公式：见文]的切空间上的投影。