Journal article
LARGE TIME BEHAVIOR AND DIFFUSION LIMIT FOR A SYSTEM OF BALANCE LAWS FROM CHEMOTAXIS IN MULTI-DIMENSIONS
Communications in mathematical sciences, Vol.19(1), pp.229-272
01/01/2021
DOI: 10.4310/CMS.2021.v19.n1.a10
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.
Details
- Title: Subtitle
- LARGE TIME BEHAVIOR AND DIFFUSION LIMIT FOR A SYSTEM OF BALANCE LAWS FROM CHEMOTAXIS IN MULTI-DIMENSIONS
- Creators
- Tong Li - University of IowaDehua Wang - University of PittsburghFang Wang - Changsha University of Science and TechnologyZhi-An Wang - Hong Kong Polytechnic UniversityKun Zhao - Tulane University
- Resource Type
- Journal article
- Publication Details
- Communications in mathematical sciences, Vol.19(1), pp.229-272
- Publisher
- INT PRESS BOSTON, INC
- DOI
- 10.4310/CMS.2021.v19.n1.a10
- ISSN
- 1539-6746
- eISSN
- 1945-0796
- Number of pages
- 44
- Grant note
- 2019JJ50659 / Natural Science Foundation of Hunan Province; Natural Science Foundation of Hunan Province 413028 / Simons Foundation Collaboration Grant for Mathematicians 2019IC39 / Double First-class International Cooperation Expansion Project DMS-1613213; DMS-1907519 / National Science Foundation; National Science Foundation (NSF) 12001064 / National Natural Science Foundation of China; National Natural Science Foundation of China (NSFC) PolyU 153031/17P; P0005368 / Hong Kong RGC GRF; Hong Kong Research Grants Council P0001905 / internal grant ZZHY 20B006 / Hunan Provincial Education Department Project
- Language
- English
- Date published
- 01/01/2021
- Academic Unit
- Mathematics
- Record Identifier
- 9984240861802771
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