We prove that the entropy for an L∞-solution to a scalar con-servation 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
Marconi E.
2016
Abstract
We prove that the entropy for an L∞-solution to a scalar con-servation 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.
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