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Algebraic contraction rate for distance between entropy solutions of scalar conservation laws
Elias Esselborn, Nicola Gigli and Felix Otto
We establish an algebraic contraction rate in a modified Wasserstein distance for solutions of scalar conservation laws with uniformly convex flux. We also show that our estimate is optimal w.r.t. scaling in time and discuss why it gives non-trivial information in relation to the stability of the rarefaction wave.