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Conservation laws with discontinuous coefficients

Abstract In order to model phenomena arising in matter flows in electromagnetic fields, engineers join systems of conservation laws with discontinuous coefficients. The simplest quasi-linear equation is u t  +  a ( f ( u )) x  = 0, where a is a given discontinuous coefficient function and f is a smooth function. We begin our study by solving the Riemann problem, and then we construct a numerical scheme of Godunov type.