Nonlinear anisotropic degenerate parabolic-hyperbolic equations with stochastic forcing

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