Scalar conservation laws with rough (stochastic) fluxes; the spatially dependent case

However with an additional control g(t) as in (1.1) and with f (z) = z 2 2 (Burgers equation), Chapouly showed in [9] that in the framework of classical solutions, any state

After a short introduction to scalar conservation laws and stochastic differential equations, we give the proof of the existence of an invariant measure for the stoschastic

• Arnaud Debussche et Julien Vovelle [ DV10b ] ou [ DV14 ] pour leur article de référence, base de réflexion pour mon mémoire de M2 et origine de cette thèse « Scalar

inhomogeneous scalar conservation law; discontinuous flux; change of variables; entropy solution; vanishing viscosity approximation; well-posedness; crossing

In such a paper, the authors were interested in the discretization of a nonlinear hyperbolic equation and proved the convergence of the solution given by an upwind finite volume

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

Keywords: Stochastic partial differential equations, conservation laws, kinetic formulation, invariant measure.. MSC: 60H15

Our result is applied to the convergence of the finite volume method in the companion paper (Dotti and Vovelle in Convergence of the finite volume method for scalar conservation