On Quantitative Compactness Estimates for Hyperbolic Conservation Laws
نویسندگان
چکیده
We are concerned with the compactness in Lloc of the semigroup (St)t≥0 of entropy weak solutions generated by hyperbolic conservation laws in one space dimension. This note provides a survey of recent results establishing upper and lower estimates for the Kolmogorov ε-entropy of the image through the mapping St of bounded sets in L1 ∩ L∞, both in the case of scalar and of systems of conservation laws. As suggested by Lax [16], these quantitative compactness estimates could provide a measure of the order of “resolution” of the numerical methods implemented for these equations.
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