@article{e557b2286adf4946b87e2abc911c581d,
title = "Large time behavior and diffusion limit for a system of balance laws from chemotaxis in multi-dimensions",
abstract = "We consider the Cauchy problem for a system of balance laws derived from a chemotaxis model with singular sensitivity in multiple space dimensions. Utilizing energy methods, we first prove the global well-posedness of classical solutions to the Cauchy problem when only the energy of the first order spatial derivatives of the initial data is sufficiently small, and the solutions are shown to converge to the prescribed constant equilibrium states as time goes to infinity. Then we prove that the solutions of the fully dissipative model converge to those of the corresponding partially dissipative model when the chemical diffusion coefficient tends to zero.",
keywords = "diffusion limit, global well-posedness, long-time behavior, System of balance laws",
author = "Tong Li and Dehua Wang and Fang Wang and Wang, {Zhi An} and Kun Zhao",
note = "Funding Information: Acknowledgments. The authors would like to thank the anonymous referee for constructive comments and suggestions which helped improve the paper. D. Wang was partially supported by the National Science Foundation under grants DMS-1613213 and DMS-1907519. F. Wang was partially supported by the National Natural Science Foundation of China (No. 12001064), the Natural Science Foundation of Hunan Province (No. 2019JJ50659), the Hunan Provincial Education Department Project (No.20B006), and the Double First-class International Cooperation Expansion Project (No. 2019IC39). Z.A. Wang was supported by the the Hong Kong RGC GRF grant No. PolyU 153031/17P (Project ID:P0005368) and internal grant ZZHY (Project ID:P0001905). K. Zhao was partially supported by the Simons Foundation Collaboration Grant for Mathematicians (No. 413028). Publisher Copyright: {\textcopyright} 2021 International Press. All Rights Reserved.",
year = "2021",
month = mar,
day = "24",
doi = "10.4310/CMS.2021.v19.n1.a10",
language = "English",
volume = "19",
pages = "229--272",
journal = "Communications in Mathematical Sciences",
issn = "1539-6746",
publisher = "International Press of Boston, Inc.",
number = "1",
}