We provide an entropy formulation for porous medium-type equations with a stochastic, non-
linear, spatially inhomogeneous forcing. Well-posedness and L 1-contraction is obtained in …

We develop a general framework for the analysis of approximations to stochastic scalar
conservation laws. Our aim is to prove, under minimal consistency properties and bounds …

In this article, we explore some of the main mathematical problems connected to
multidimensional fractional conservation laws driven by Lévy processes. Making use of an …

In this paper, we are concerned with an operator-splitting scheme for linear fractional and
fractional degenerate stochastic conservation laws driven by multiplicative Lévy noise. More …

We analyse a semidiscrete splitting method for conservation laws driven by a semilinear
noise term. Making use of fractional bounded variation (BV) estimates, we show that the …

In this article, we study the homogeneous Dirichlet problem for a degenerate parabolic-
hyperbolic PDE perturbed by Levy noise. In particular, we develop the well-posedness …

Under a standard CFL condition, we prove the convergence of the explicit-in-time Finite
Volume method with monotone fluxes for the approximation of scalar first-order conservation …

We are interested in multi-dimensional nonlinear scalar conservation laws forced by a
multiplicative stochastic noise with a general time and space dependent flux-function. We …

We are concerned with nonlinear anisotropic degenerate parabolic-hyperbolic equations
with stochastic forcing, which are heterogeneous (ie, not space-translational invariant). A …

Some recent developments in the analysis of long-time behaviors of stochastic solutions of
nonlinear conservation laws driven by stochastic forcing are surveyed. The existence and …