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 unique solution,â€¦ (More)

Abstract We consider the fractal Burgers equation (that is to say the Burgers equation to which is added a fractional power of the Laplacian) and we prove that, if the power of the Laplacian involvedâ€¦ (More)

The interest of such an equation (namely Equation (1.1)) was pointed out to us by Paul Clavin in the context of pattern formation in detonation waves. The study of detonations leads, in a firstâ€¦ (More)

Abstract. In this paper, we study the Cauchy problem for a quasilinear degenerate parabolic stochastic partial differential equation driven by a cylindrical Wiener process. In particular, we adaptâ€¦ (More)

We study the limit of a kinetic evolution equation involving a small parameter and perturbed by a smooth random term which also involves the small parameter. Generalizing the classical method ofâ€¦ (More)

Under an hypothesis of non-degeneracy of the flux, we study the long-time behaviour of periodic scalar first-order conservation laws with stochastic forcing in any space dimension. For sub-cubicâ€¦ (More)

We study the BGK approximation to first-order scalar conservation laws with a flux which is discontinuous in the space variable. We show that the Cauchy Problem for the BGK approximation isâ€¦ (More)

We consider the long-time behavior of the entropy solution of a first-order scalar conservation law on a Riemannian manifold. In the case of the Torus, we show that, under a weak property of genuineâ€¦ (More)