The full history recursive multilevel Picard approximation method for semilinear parabolic partial differential equations (PDEs) is the only method which provably overcomes the curse of dimensionality for general time horizons if the coefficient functions and the nonlinearity are globally Lipschitz continuous and the nonlinearity is gradient-independent. In this article we extend this result to locally monotone coefficient functions. Our results cover a range of semilinear PDEs with polynomial coefficient functions.

翻译：如果系数函数和非线性是全球Lipschitz连续的,非线性是梯度独立的,则整个历史的半线性抛物线部分偏差方程(PDEs)递归多级Picard近似法是唯一可以克服一般时空线的维度诅咒的方法。在本条中,我们将这一结果扩展至本地单体系数函数。我们的结果涵盖了一系列具有多元系数函数的半线性PDEs。