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,\inf...

We propose a second order finite volume scheme for nonlinear degenerate parabolic equations. For some of these models (porous media equation, drift-diffusion system for semiconductors, ...) it has been proved that the transient solution converges to a steady-state when time goes to infinity. The present scheme preserves steady-states and provides a satisfying long-time behavior. Moreover, it re...

This is the second article of the two papers, in which we investigate the holomorphic and formal flattening problem of a non-degenerate CR singular point of a codimension two real submanifold in C with n ≥ 3. The problem is motivated from the study of the complex Plateau problem that looks for the Levi-flat hypersurface bounded by a given real submanifold and by the classical complex analysis p...