We are concerned with nonlinear anisotropic degenerate parabolic-hyperbolic equations with stochastic forcing, which are heterogeneous (i.e., not space-translational invariant). A unified framework is established for the continuous dependence estimates, fractional BV regularity estimates, and well-posedness for stochastic kinetic solutions of the nonlinear stochastic degenerate parabolic-hyperbolic equation. In particular, we establish the well-posedness of the nonlinear stochastic equation in $L^p\cap N^{\kappa ,1}$ for $p\in [1,\infty )$ and the κ–Nikolskii space $N^{\kappa ,1}$ with $\kappa \in (0,1]$, and the $L^1$–continuous dependence of the stochastic kinetic solutions not only on the initial data, but also on the degenerate diffusion matrix function, the flux function, and the multiplicative noise function involved in the nonlinear equation.

我们关注具有随机强迫的非线性各向异性退化抛物线-双曲方程，它们是异质的（即，不是空间平移不变的）。为非线性随机退化抛物双曲方程的随机动力学解的连续依赖估计、分数BV正则性估计和适定性建立了统一的框架。特别地，我们建立了非线性随机方程的适定性${升}^{磷}\cap N^{\kappa ,1}$ 为了 $磷\in [1,\infty )$和κ- Nikolskii 空间$N^{\kappa ,1}$ 和 $\kappa \in (0,1]$，以及 ${升}^1$– 随机动力学解的连续依赖性不仅取决于初始数据，而且还取决于非线性方程中涉及的退化扩散矩阵函数、通量函数和乘法噪声函数。