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

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

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