Abstract:We focus on entropy admissible solutions of scalar conservation laws in one space dimension and establish new regularity results with respect to time. First, we assume that the flux function f is strictly convex and show that, for every x \in \BbbR , the total variation of the composite function f \circ u(\cdot , x) is controlled by the total variation of the initial datum. Next, we assume that f is monotone and, under no convexity assumption, we show that, for every x, the total variation of the left and the … Show more
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