Semi-discretization for Stochastic Scalar Conservation Laws with Multiple Rough Fluxes

Benjamin Gess (1) , Benoît Perthame (2, 3) , Panagiotis E. Souganidis (4)

1 Universität Bielefeld = Bielefeld University
2 MAMBA - Modelling and Analysis for Medical and Biological Applications
3 LJLL - Laboratoire Jacques-Louis Lions
4 Department of Mathematics [Chicago]

We develop a semi-discretization approximation for scalar conservation laws with multiple rough time dependence in inhomogeneous fluxes. The method is based on Brenier's transport-collapse algorithm and uses characteristics defined in the setting of rough paths. We prove strong L 1-convergence for inhomogeneous fluxes and provide a rate of convergence for homogeneous one's. The approximation scheme as well as the proofs are based on the recently developed theory of path-wise entropy solutions and uses the kinetic formulation which allows to define globally the (rough) characteristics.

Domaines: Equations aux dérivées partielles [math.AP]

Benjamin Gess, Benoît Perthame, Panagiotis E. Souganidis. Semi-discretization for Stochastic Scalar Conservation Laws with Multiple Rough Fluxes. SIAM Journal on Numerical Analysis, 2016, 54 (4), pp.2187-2209. ⟨10.1137/15M1053670⟩. ⟨hal-01481284⟩