We present in this note a local in time well-posedness result for the singular 2-dimensional quasilinear generalized parabolic Anderson model equation$$\begin{aligned} \partial _t u - a(u)\Delta u = g(u)\xi . \end{aligned}$$The key idea of our approach is a simple transformation of the equation which allows to treat the problem as a semilinear problem. The analysis is done within the elementary setting of paracontrolled calculus.

中文翻译：

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拟线性广义抛物型Anderson模型方程

我们在此笔记中给出了奇异二维拟线性广义抛物线安德森模型方程$$ \ begin {aligned \\ partial_t u-a（u）\ Delta u = g（u）\ xi \ end {aligned} $$我们方法的关键思想是方程的简单转换，可以将问题视为半线性问题。分析是在基本控制演算的基本设置内完成的。