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The generalized BBM-Burgers equations: convergence results for conservation law with discontinuous flux function

We consider conservation laws with discontinuous flux, which are regularized with generalized BBM-Burgers equations. We study the convergence of one sequence of solutions of these equations for one solution of the associated conservation law. In the multidimensional case, we prove one convergence result using the H-measures and in the one-dimensional case, we use the method of compensated compactness.