Nonlinear anisotropic degenerate parabolic-hyperbolic equations with stochastic forcing

摘要

We are concerned with nonlinear anisotropic degenerate parabolic-hyperbolic equations with stochastic forcing, which are heterogeneous (i.e., not space-translational invariant). Aunified framework is established for the continuous dependence estimates, fractional BVregularity estimates, and wellposedness 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 boolean AND N-kappa,N-1 for p epsilon [1, infinity) and the kappa-Nikolskii space N-kappa,N-1 with kappa epsilon (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. (C) 2021 Elsevier Inc. All rights reserved.