LARGE TIME BEHAVIOR AND DIFFUSION LIMIT FOR A SYSTEM OF BALANCE LAWS FROM CHEMOTAXIS IN MULTI-DIMENSIONS

Tong Li, Dehua Wang, Fang Wang, Zhi An Wang, Kun Zhao

Research output: Journal article publicationJournal articleAcademic researchpeer-review

1 Citation (Scopus)

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.

Original languageEnglish
Pages (from-to)229-272
Number of pages44
JournalCommunications in Mathematical Sciences
Volume19
Issue number1
DOIs
Publication statusPublished - 24 Mar 2021

Keywords

  • diffusion limit
  • global well-posedness
  • long-time behavior
  • System of balance laws

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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