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Sturm attractors for quasilinear parabolic equations with singular coefficients

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Phillipo Lappicy

Dynamical Systems · Submitted 11 Jun 2018

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

The authors' main claim In particular, we construct heteroclinic connections between hyperbolic equilibria, stating necessary and sufficient conditions for heteroclinics to occur.

how it is stated · asserted 1.00 read the record →

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arXiv ID1806.04019 (version 2)
Pith ID3ITZSI7F, Pith's permanent record of this paper and its review
CitationPhillipo Lappicy. "Sturm attractors for quasilinear parabolic equations with singular coefficients." arXiv:1806.04019 (2018). https://pith.science/paper/3ITZSI7F
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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, 3,657 input tokens.

What the abstract itself states, as probabilities: claims first 0.12 · states limitation 0.11 · human participants 0.01 · controlled comparison 0.03 · randomized assignment 0.01 · states quantitative result 0.07 · compares with prior results 0.94 · mentions code or data availability 0.02.

The abstract, sentence by sentence

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

The goal of this paper is to construct explicitly the global attractors of parabolic equations with singular diffusion coefficients on the boundary, as it was done without the singular term for the semilinear case by Brunovsk'y and Fiedler (1986), generalized by Fiedler and Rocha (1996) and later for quasilinear equa- tions by the author (2017). In particular, we construct heteroclinic connections between hyperbolic equilibria, stating necessary and sufficient conditions for heteroclinics to occur. Such conditions can be computed through a permutation of the equilibria. Lastly, an example is computed yielding the well known Chafee-Infante attractor.

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 The goal of this paper is to construct explicitly the global attractors of parabolic equations with singular diffusion coefficients on the boundary, as it was done without the singular term for the semilinear case by Brunovsk'y and Fiedler (1986), generalized by Fiedler and Rocha (1996) and later for quasilinear equa- tions by the author (2017). contribution 0.76 0.51 0.37 asserted 0.99
s1 In particular, we construct heteroclinic connections between hyperbolic equilibria, stating necessary and sufficient conditions for heteroclinics to occur. contribution 0.83 0.94 0.37 asserted 1.00
s2 Such conditions can be computed through a permutation of the equilibria. method 0.87 0.68 0.11 asserted 0.94
s3 Lastly, an example is computed yielding the well known Chafee-Infante attractor. result 0.83 0.90 0.10 asserted 1.00

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

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  • C citations
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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

The goal of this paper is to construct explicitly the global attractors of parabolic equations with singular diffusion coefficients on the boundary, as it was done without the singular term for the semilinear case by Brunovsk'y and Fiedler (1986), generalized by Fiedler and Rocha (1996) and later for quasilinear equa- tions by the author (2017). In particular, we construct heteroclinic connections between hyperbolic equilibria, stating necessary and sufficient conditions for heteroclinics to occur. Such conditions can be computed through a permutation of the equilibria. Lastly, an example is computed yielding the well known Chafee-Infante attractor.

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2 arXiv papers cite this in 5 sentences

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Cites it as support 1 paper

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