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Pseudo-Differential Equations with Weak Degeneration for Radial Functions of $p$-adic Argument

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Alexandra V. Antoniouk, Anatoly N. Kochubei, Mariia V. Serdiuk

Classical Analysis and ODEs · Submitted 13 Mar 2022

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

The authors' main claim Under various assumptions, we prove the local existence and uniqueness of mild solutions, existence of their global extensions and a regularity property.

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arXiv ID2203.06623 (version 2)
Pith IDKYEZTBRO, Pith's permanent record of this paper and its review
CitationAlexandra V. Antoniouk, Anatoly N. Kochubei, Mariia V. Serdiuk. "Pseudo-Differential Equations with Weak Degeneration for Radial Functions of $p$-adic Argument." arXiv:2203.06623 (2022). https://pith.science/paper/KYEZTBRO
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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 4,270 input tokens.

What the abstract itself states, as probabilities: claims first 0.06 · states limitation 0.27 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.05 · compares with prior results 0.62 · mentions code or data availability 0.02.

The abstract, sentence by sentence

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

In earlier papers (A. N. Kochubei, Pacif. J. Math., 269 (2014), 355-369; J. Math. Anal. Appl.483 (2020), Article 123609), one of the authors developed a theory of pseudo-differential equations for radial real-valued functions on a non-Archimedean local field, with some features resembling those of classical ordinary differential equations. Here we consider equations of this kind, but with a weak degeneration. Under various assumptions, we prove the local existence and uniqueness of mild solutions, existence of their global extensions and a regularity property.

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 earlier papers (A. N. Kochubei, Pacif. background 1.00 0.08 0.01 unclear 0.87
s1 J. Math., 269 (2014), 355-369; J. Math. Anal. background 1.00 0.05 0.02 unclear 0.98
s2 Appl.483 (2020), Article 123609), one of the authors developed a theory of pseudo-differential equations for radial real-valued functions on a non-Archimedean local field, with some features resembling those of classical ordinary differential equations. background 1.00 0.19 0.06 asserted 0.98
s3 Here we consider equations of this kind, but with a weak degeneration. contribution 0.92 0.51 0.06 asserted 0.94
s4 Under various assumptions, we prove the local existence and uniqueness of mild solutions, existence of their global extensions and a regularity property. result 0.86 0.95 0.85 asserted 1.00

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

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  • T body sentences
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  • 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 earlier papers (A. N. Kochubei, Pacif. J. Math., 269 (2014), 355-369; J. Math. Anal. Appl.483 (2020), Article 123609), one of the authors developed a theory of pseudo-differential equations for radial real-valued functions on a non-Archimedean local field, with some features resembling those of classical ordinary differential equations. Here we consider equations of this kind, but with a weak degeneration. Under various assumptions, we prove the local existence and uniqueness of mild solutions, existence of their global extensions and a regularity property.

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