Heat equation is a partial differential equation describing the temperature change of an object with time. In the traditional heat equation, the strength of heat source is assumed to be certain. However, in practical application, the heat source is usually influenced by noise. To describe the noise, some researchers tried to employ a tool called Winner process. Unfortunately, it is unreasonable to apply Winner process in probability theory to modeling noise in heat equation because the change rate of temperature will tend to infinity. Thus, we employ Liu process in uncertainty theory to characterize the noise. By modeling the noise via Liu process, the one-dimensional uncertain heat equation was constructed. Since the real world is a three-dimensional space, the paper extends the one-dimensional uncertain heat equation to a three-dimensional uncertain heat equation. Later, the solution of the three-dimensional uncertain heat equation and the inverse uncertainty distribution of the solution are given. At last, a paradox of stochastic heat equation is introduced.

中文翻译：

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三维不确定热方程

热方程是描述物体温度随时间变化的偏微分方程。在传统的热方程中，假设热源的强度是确定的。但在实际应用中，热源通常会受到噪声的影响。为了描述噪音，一些研究人员尝试使用一种称为Winner process 的工具。不幸的是，将概率论中的Winner过程应用于热方程中的噪声建模是不合理的，因为温度的变化率将趋于无穷大。因此，我们采用不确定性理论中的刘过程来表征噪声。通过Liu过程对噪声进行建模，构建了一维不确定热方程。由于现实世界是一个三维空间，本文将一维不确定热方程扩展为三维不确定热方程。随后给出了三维不确定热方程的解和解的逆不确定性分布。最后，引入了随机热方程的一个悖论。