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Improved stability estimates on general scalar balance laws

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Paper breakdownThe authors' claims, conditions and measurements, as JSON Signed receiptProof this review has not been altered
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Magali Lécureux-Mercier (TECHNION)

Analysis of PDEs · Submitted 25 Oct 2010

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

The authors' main claim The improvements are twofold: first the expression of the coefficients in these estimates are more precise; second, we eliminate some regularity hypotheses thus extending significantly the applicability of our estimates.

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arXiv ID1010.5116 (version 2)
Pith ID4JLM3NSH, Pith's permanent record of this paper and its review
CitationMagali L\'ecureux-Mercier (TECHNION). "Improved stability estimates on general scalar balance laws." arXiv:1010.5116 (2010). https://pith.science/paper/4JLM3NSH
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Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 2,994 input tokens, $0.0001 reported.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.11 · human participants 0.01 · controlled comparison 0.06 · randomized assignment 0.01 · states quantitative result 0.09 · compares with prior results 0.93 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v2. Results and the main claim are underlined; .

Consider the general scalar balance law $\partial_t u + \mathrm{Div} f(t, x, u) = F(t, x, u)$ in several space dimensions. The aim of this note is to improve the results of Colombo, Mercier, Rosini who gave an estimate of the dependence of the solutions from the flow f and from the source F. The improvements are twofold: first the expression of the coefficients in these estimates are more precise; second, we eliminate some regularity hypotheses thus extending significantly the applicability of our estimates.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 Consider the general scalar balance law $\partial_t u + \mathrm{Div} f(t, x, u) = F(t, x, u)$ in several space dimensions. background 1.00 0.11 0.03 unclear 0.58
s1 The aim of this note is to improve the results of Colombo, Mercier, Rosini who gave an estimate of the dependence of the solutions from the flow f and from the source F. contribution 0.67 0.12 0.12 asserted 0.94
s2 The improvements are twofold: first the expression of the coefficients in these estimates are more precise; second, we eliminate some regularity hypotheses thus extending significantly the applicability of our estimates. contribution 0.97 0.93 0.65 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 0.99.

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Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

Consider the general scalar balance law $\partial_t u + \mathrm{Div} f(t, x, u) = F(t, x, u)$ in several space dimensions. The aim of this note is to improve the results of Colombo, Mercier, Rosini who gave an estimate of the dependence of the solutions from the flow f and from the source F. The improvements are twofold: first the expression of the coefficients in these estimates are more precise; second, we eliminate some regularity hypotheses thus extending significantly the applicability of our estimates.

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