We give a Wong-Zakai type characterisation of the solutions of quasilinear heat equations driven by space-time white noise in $1+1$ dimensions. In order to show that the renormalisation counterterms are local in the solution, a careful arrangement of a few hundred terms is required. The main tool in this computation is a general ‘integration by parts’ formula that provides a number of linear identities for the renormalisation constants.

中文翻译：

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时空白噪声驱动的非散度型拟线性热方程

我们给出了时空白噪声驱动的准​​线性热方程解的Wong-Zakai型刻画 $\mathrm{1个}+\mathrm{1个}$尺寸。为了表明重归一化对等项在解决方案中是局部的，需要仔细安排几百个项。该计算的主要工具是通用的“零件积分”公式，该公式为重归一化常数提供了许多线性恒等式。