We show that the Cauchy Problem for a randomly forced, periodic multi-dimensional scalar
first-order conservation law with additive or multiplicative noise is well posed: it admits a …

We present a numerical method for approximating the solutions of degenerate parabolic
equations with a formal gradient flow structure. The numerical method we propose …

The nonlinear systems obtained by discretizing degenerate parabolic equations may be
hard to solve, especially with Newton's method. In this paper, we apply to the Richards …

In this work, we present a mass conservative numerical scheme for two-phase flow in porous
media. The model for flow consists of two fully coupled, nonlinear equations: a degenerate …

For the hyperbolic conservation laws with discontinuous-flux function, there may exist
several consistent notions of entropy solutions; the difference between them lies in the …

In this paper we derive an a posteriori error estimate for the numerical approximation of the
solution of a system modeling the flow of two incompressible and immiscible fluids in a …

We consider the system of equations governing an incompressible immiscible two-phase
flow within a heterogeneous porous medium made of two different rock types. Since the …

We study a one-dimensional model for two-phase flows in heterogeneous media, in which
the capillary pressure functions can be discontinuous with respect to space. We first give a …

Scalar conservation law∂ t ρ (t, x)+∂ x (f (t, x, ρ))= 0 with a flux C 1 in the state variable ρ,
piecewise C 1 in the (t, x)-plane admits infinitely many consistent notions of solution which …

This paper deals with the one-dimensional formulation of Hughes' model for pedestrian
flows in the setting of entropy solutions. In this model, the mass conservation equation for the …