论文标题
具有局部单调系数函数的高维半线性部分微分方程的多级PICARD近似值
Multilevel Picard approximations of high-dimensional semilinear partial differential equations with locally monotone coefficient functions
论文作者
论文摘要
半连接抛物线偏微分方程（PDE）的完整历史递归多级PICARD近似方法是唯一的方法，如果系数函数和非线性是全球性的Lipschitz持续性，并且非线性且非线性是梯度依赖性的，则可以在一般时间范围内克服尺寸范围的诅咒。在本文中，我们将此结果扩展到局部单调系数函数。我们的结果涵盖了具有多项式系数函数的一系列半线性PDE。
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.
