Optimal Regularizing Effect for Scalar Conservation Laws

Beno\^it Perthame; Fran\c{c}ois Golse

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Optimal Regularizing Effect for Scalar Conservation Laws

François Golse, Benoît Perthame

Analysis of PDEs · Submitted 10 Dec 2011

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim We investigate the regularity of bounded weak solutions of scalar conservation laws with uniformly convex flux in space dimension one, satisfying an entropy condition with entropy production term that is a signed Radon measure.

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We investigate the regularity of bounded weak solutions of scalar conservation laws with uniformly convex flux in space dimension one, satisfying an entropy condition with entropy production term that is a signed Radon measure. The proof is based on the kinetic formulation of scalar conservation laws and on an interaction estimate in physical space.

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#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We investigate the regularity of bounded weak solutions of scalar conservation laws with uniformly convex flux in space dimension one, satisfying an entropy condition with entropy production term that is a signed Radon measure.	contribution 0.93	0.75	0.14	asserted 0.69
s1	The proof is based on the kinetic formulation of scalar conservation laws and on an interaction estimate in physical space.	method 1.00	0.75	0.04	asserted 1.00

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The paper

Original abstract

We investigate the regularity of bounded weak solutions of scalar conservation laws with uniformly convex flux in space dimension one, satisfying an entropy condition with entropy production term that is a signed Radon measure. The proof is based on the kinetic formulation of scalar conservation laws and on an interaction estimate in physical space.

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3 arXiv papers cite this in 7 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 5 sentences without a confident label

Compares with it 1 paper

In [ref] the result is restricted for uniform convex flux and in the one dimensional case.

High frequency waves and the maximal smoothing effect for nonlinear scalar conservation laws · The smoothing effect in Sobolev spaces · 0.86

Cites it as background 1 paper

For recent other approaches we refer the reader to [ref] .

Oscillating waves and optimal smoothing effect for one-dimensional nonlinear scalar conservation laws · Introduction and nonlinear flux definitions · 1.00

What it cites

Cites as background 1 paper

Agoshkov [ref] ) and in a series of subsequent contributions by several authors where more and more general classes of functions $f$ and right hand sides are considered: see in particular [ref] .

Concentrations in kinetic transport equations and hypoellipticity · Velocity Averaging in Physical Space · 0.86

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