In this paper we propose a time-splitting method for degenerate convection–diffusion equations perturbed stochastically by white noise. This work generalizes previous results on splitting operator techniques for stochastic hyperbolic conservation laws for the degenerate parabolic case. The convergence in Llocp$\begin{array}{} \displaystyle L^p_{\rm loc} \end{array}$ of the time-splitting operator scheme to the unique weak entropy solution is proven. Moreover, we analyze the performance of the splitting approximation by computing its convergence rate and showing numerical simulations for some benchmark examples, including a fluid flow application in porous media.

中文翻译：

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退化对流扩散方程随机来源时间分裂近似的收敛性

在本文中，我们提出了一种由白噪声随机扰动的退化对流扩散方程的时间分解方法。这项工作概括了关于退化抛物线情形的随机双曲守恒律的分裂算子技术的先前结果。证明了时间分解算子方案的Llocp $ \ begin {array} {} \ displaystyle L ^ p _ {\ rm loc} \ end {array} $收敛到唯一的弱熵解。此外，我们通过计算分裂近似值的收敛速度并分析了一些基准示例（包括在多孔介质中的流体应用）的数值模拟，来分析分裂近似的性能。