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The evolution to localized and front solutions in a non-Lipschitz reaction-diffusion Cauchy problem with trivial initial data

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John Christopher Meyer, David John Needham

Analysis of PDEs · Submitted 28 Jul 2016

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

The authors' main claim In this paper, we establish the existence of spatially inhomogeneous classical self-similar solutions to a non-Lipschitz semi-linear parabolic Cauchy problem with trivial initial data.

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arXiv ID1607.08423 (version 1)
Pith ID36C6OLQC, Pith's permanent record of this paper and its review
CitationDavid John Needham, John Christopher Meyer. "The evolution to localized and front solutions in a non-Lipschitz reaction-diffusion Cauchy problem with trivial initial data." arXiv:1607.08423 (2016). https://pith.science/paper/36C6OLQC
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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,057 input tokens.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.14 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.51 · compares with prior results 0.04 · mentions code or data availability 0.01.

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

In this paper, we establish the existence of spatially inhomogeneous classical self-similar solutions to a non-Lipschitz semi-linear parabolic Cauchy problem with trivial initial data. Specifically we consider bounded solutions to an associated two-dimensional non-Lipschitz non-autonomous dynamical system, for which, we establish the existence of a two-parameter family of homoclinic connections on the origin, and a heteroclinic connection between two equilibrium points. Additionally, we obtain bounds and estimates on the rate of convergence of the homoclinic connections to the origin.

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#sentencerolethe authors' own workstates the main conclusionstrength
s0 In this paper, we establish the existence of spatially inhomogeneous classical self-similar solutions to a non-Lipschitz semi-linear parabolic Cauchy problem with trivial initial data. result 0.54 0.96 0.85 asserted 1.00
s1 Specifically we consider bounded solutions to an associated two-dimensional non-Lipschitz non-autonomous dynamical system, for which, we establish the existence of a two-parameter family of homoclinic connections on the origin, and a heteroclinic connection between two equilibrium points. result 0.37 0.94 0.14 asserted 1.00
s2 Additionally, we obtain bounds and estimates on the rate of convergence of the homoclinic connections to the origin. result 0.94 0.95 0.07 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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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

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Original abstract

In this paper, we establish the existence of spatially inhomogeneous classical self-similar solutions to a non-Lipschitz semi-linear parabolic Cauchy problem with trivial initial data. Specifically we consider bounded solutions to an associated two-dimensional non-Lipschitz non-autonomous dynamical system, for which, we establish the existence of a two-parameter family of homoclinic connections on the origin, and a heteroclinic connection between two equilibrium points. Additionally, we obtain bounds and estimates on the rate of convergence of the homoclinic connections to the origin.

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