@article{cb51946b15514893b3c5341af0401c58,
title = "A note on construction of nonnegative initial data inducing unbounded solutions to some two-dimensional Keller-Segel systems",
abstract = "It was shown that unbounded solutions of the Neumann initial-boundary value problem to the two-dimensional Keller-Segel system can be induced by initial data having large negative energy if the total mass Λ ∈ (4π, ∞) \ 4π · N and an example of such an initial datum was given for some transformed system and its associated energy in Horstmann-Wang (2001). In this work, we provide an alternative construction of nonnegative nonradially symmetric initial data enforcing unbounded solutions to the original Keller-Segel model.",
keywords = "Chemotaxis, Infinite-time blow-up, Keller-Segel system, Local sensing, Lyapunov functional, Unbounded solution",
author = "Kentaro Fujie and Jie Jiang",
note = "Funding Information: The authors thank the anonymous referee{\textquoteright}s careful reading and useful suggestions. K. Fujie is supported by Japan Society for the Promotion of Science (Grant-in-Aid for Early-Career Scientists; No. 19K14576). J. Jiang is supported by Hubei Provincial Natural Science Foundation under the grant No. 2020CFB602. Publisher Copyright: {\textcopyright} 2022 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)",
year = "2022",
doi = "10.3934/MINE.2022045",
language = "English",
volume = "4",
pages = "1--12",
journal = "Mathematics In Engineering",
issn = "2640-3501",
publisher = "American Institute of Mathematical Sciences",
number = "6",
}