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The Ostrovsky Hunter equation with a space dependent flux function

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Neelabja Chatterjee, Nils Henrik Risebro

Numerical Analysis · Submitted 20 Dec 2018

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

The authors' main claim Our main results are that if the flux function is twice differentiable, then there exists a unique entropy solution.

how it is stated · asserted 1.00 read the record →

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arXiv ID1812.08463 (version 1)
Pith IDL7RV2XMS, Pith's permanent record of this paper and its review
CitationNeelabja Chatterjee, Nils Henrik Risebro. "The Ostrovsky Hunter equation with a space dependent flux function." arXiv:1812.08463 (2018). https://pith.science/paper/L7RV2XMS
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The compiled record

The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 2,919 input tokens.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.50 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.95 · compares with prior results 0.10 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; .

We study the periodic Ostrovsky-Hunter equation in the case where the flux function may depend on the spatial variable. Our main results are that if the flux function is twice differentiable, then there exists a unique entropy solution. This entropy solution may be constructed as a limit of approximate solutions generated by a finite volume scheme, and the finite volume approximations converge to the entropy solution at a rate 1/2.

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 We study the periodic Ostrovsky-Hunter equation in the case where the flux function may depend on the spatial variable. contribution 0.71 0.77 0.03 asserted 0.71
s1 Our main results are that if the flux function is twice differentiable, then there exists a unique entropy solution. result 1.00 0.92 0.86 asserted 1.00
s2 This entropy solution may be constructed as a limit of approximate solutions generated by a finite volume scheme, and the finite volume approximations converge to the entropy solution at a rate 1/2. result 0.86 0.88 0.28 hedged possibility 0.64

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

What was examined, and what was not

sources read
  • arXiv listing abstract v1
not examined
  • full text
  • figures and tables
  • references and citing sentences
  • relations to other papers
levels run
  • P abstract
not run
  • S sections
  • T body sentences
  • C citations
  • R cross-paper relations

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

We study the periodic Ostrovsky-Hunter equation in the case where the flux function may depend on the spatial variable. Our main results are that if the flux function is twice differentiable, then there exists a unique entropy solution. This entropy solution may be constructed as a limit of approximate solutions generated by a finite volume scheme, and the finite volume approximations converge to the entropy solution at a rate 1/2.

Human review

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How the literature uses it

1 arXiv paper cite this in 1 sentence

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 whose main result relates to this one's

Found among the papers closest to this one by title and main claim. Pith's classifier compared each pair's main results and a second model family confirmed the relation; checked against two further families, shown conflicts agreed 118 times in 120 and shown same results 218 times in 239. The quoted sentence is the other paper's main claim.

States the same result 1 paper

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