We are concerned with the compactness in L^1_loc 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 "-entropy of the image through the mapping S_t of bounded sets in L^1 \cap L^\infty, 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.

On quantitative compactness estimates for hyperbolic conservation laws

ANCONA, FABIO;
2014

Abstract

We are concerned with the compactness in L^1_loc 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 "-entropy of the image through the mapping S_t of bounded sets in L^1 \cap L^\infty, 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.
2014
Hyperbolic Problems: Theory, Numerics, Applications
1-60133-017-0
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11577/3188048
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