Sharp L1 stability estimates for hyperbolic conservation laws

Details Sharp L1 stability estimates for hyperbolic conservation laws Sharp L1 stability estimates for hyperbolic conservation laws

2000-06-15

arxiv.org/abs/math/0006109v2

Port. Math. 58 (2001), 1--44

Mathematics

Analysis of PDEs

30 pages

Scientific paper

In this paper, we introduce a generalization of Liu-Yang's weighted norm to linear and to nonlinear hyperbolic equations. Extending a result by Hu and LeFloch for piecewise constant solutions, we establish sharp L1 continuous dependence estimates for general solutions of bounded variation. Two different strategies are successfully investigated. On one hand, we justify passing to the limit in an L1 estimate valid for piecewise constant wave-front tracking approximations. On the other hand, we use the technique of generalized characteristics and, following closely an approach by Dafermos, we derive the sharp L1 estimate directly from the equation.

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