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Singularly perturbed degenerated parabolic equations and application to seabed morphodynamics in tided environment

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Ibrahima Faye (L.M.D.A.N), Emmanuel Frenod (Lab-STICC), Diaraf Seck (L.M.D.A.N)

Analysis of PDEs · Submitted 20 Nov 2009

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

The authors' main claim We, then give an existence and uniqueness result for the short-term and mean-term models.

how it is stated · asserted 1.00 read the record →

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arXiv ID0911.4041 (version 3)
Pith ID2O4G4CKB, Pith's permanent record of this paper and its review
CitationDiaraf Seck (L.M.D.A.N), Emmanuel Frenod (Lab-STICC), Ibrahima Faye (L.M.D.A.N). "Singularly perturbed degenerated parabolic equations and application to seabed morphodynamics in tided environment." arXiv:0911.4041 (2009). https://pith.science/paper/2O4G4CKB
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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-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 4,127 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.09 · human participants 0.02 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.05 · compares with prior results 0.04 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v3. Results and the main claim are underlined; .

In this paper we build models for short-term, mean-term and long-term dynamics of dune and megariple morphodynamics. They are models that are degenerated parabolic equations which are, moreover, singularly perturbed. We, then give an existence and uniqueness result for the short-term and mean-term models. This result is based on a time-space periodic solution existence result for degenerated parabolic equation that we set out. Finally the short-term model is homogenized.

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 In this paper we build models for short-term, mean-term and long-term dynamics of dune and megariple morphodynamics. contribution 0.97 0.92 0.10 asserted 1.00
s1 They are models that are degenerated parabolic equations which are, moreover, singularly perturbed. method 0.55 0.52 0.07 asserted 1.00
s2 We, then give an existence and uniqueness result for the short-term and mean-term models. result 0.86 0.95 0.32 asserted 1.00
s3 This result is based on a time-space periodic solution existence result for degenerated parabolic equation that we set out. method 0.71 0.91 0.12 asserted 1.00
s4 Finally the short-term model is homogenized. contribution 0.63 0.92 0.16 asserted 1.00

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

What was examined, and what was not

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  • arXiv listing abstract v3
not examined
  • full text
  • figures and tables
  • references and citing sentences
  • relations to other papers
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  • P abstract
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  • 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

In this paper we build models for short-term, mean-term and long-term dynamics of dune and megariple morphodynamics. They are models that are degenerated parabolic equations which are, moreover, singularly perturbed. We, then give an existence and uniqueness result for the short-term and mean-term models. This result is based on a time-space periodic solution existence result for degenerated parabolic equation that we set out. Finally the short-term model is homogenized.

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