We prove that the entropy for an $L^∞$-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.

10aconcentration10aConservation laws10aentropy solutions10aLagrangian representation10ashocks1 aBianchini, Stefano1 aMarconi, Elio uhttp://aimsciences.org//article/id/ce4eb91e-9553-4e8d-8c4c-868f07a315ae00336nas a2200097 4500008004100000245004100041210004100082100002000123700002300143856007200166 2015 eng d00aConvergence rate of the Glimm scheme0 aConvergence rate of the Glimm scheme1 aModena, Stefano1 aBianchini, Stefano uhttps://www.math.sissa.it/publication/convergence-rate-glimm-scheme00337nas a2200097 4500008004300000245006000043210005800103100002300161700001900184856003600203 2009 en_Ud 00aA connection between viscous profiles and singular ODEs0 aconnection between viscous profiles and singular ODEs1 aBianchini, Stefano1 aSpinolo, Laura uhttp://hdl.handle.net/1963/255500816nas a2200121 4500008004300000245005800043210005600101260004800157520040900205100002300614700002100637856003600658 2002 en_Ud 00aA center manifold technique for tracing viscous waves0 acenter manifold technique for tracing viscous waves bAmerican Institute of Mathematical Sciences3 aIn this paper we introduce a new technique for tracing viscous travelling profiles. To illustrate the method, we consider a special 2 x 2 hyperbolic system of conservation laws with viscosity, and show that any solution can be locally decomposed as the sum of 2 viscous travelling profiles. This yields the global existence, stability and uniform BV bounds for every solution with suitably small BV data.1 aBianchini, Stefano1 aBressan, Alberto uhttp://hdl.handle.net/1963/307500359nas a2200109 4500008004300000245004000043210003800083260004800121100002300169700002100192856003600213 2001 en_Ud 00aA case study in vanishing viscosity0 acase study in vanishing viscosity bAmerican Institute of Mathematical Sciences1 aBianchini, Stefano1 aBressan, Alberto uhttp://hdl.handle.net/1963/3091