We prove that the entropy for an $L^\infty$-solution to a scalar conservation laws with continuous initial data is concentrated on a countably $1$-rectifiable set. To prove this result we introduce the notion of Lagrangian representation of the solution and give regularity estimates on the solution.
On the concentration of entropy for scalar conservation laws / Bianchini, Stefano; Marconi, Elio. - In: DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS. SERIES S. - ISSN 1937-1632. - 9:1(2016), pp. 73-88. [10.3934/dcdss.2016.9.73]
On the concentration of entropy for scalar conservation laws
Bianchini, Stefano;Marconi, Elio
2016-01-01
Abstract
We prove that the entropy for an $L^\infty$-solution to a scalar conservation laws with continuous initial data is concentrated on a countably $1$-rectifiable set. To prove this result we introduce the notion of Lagrangian representation of the solution and give regularity estimates on the solution.File in questo prodotto:
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