Asymptotic dynamics on a singular chemotaxis system modeling onset of tumor angiogenesis

Zhian Wang, Zhaoyin Xiang, Pei Yu

Research output: Journal article publicationJournal articleAcademic researchpeer-review

56 Citations (Scopus)

Abstract

The asymptotic behavior of solutions to a singular chemotaxis system modeling the onset of tumor angiogenesis in two and three dimensional whole spaces is investigated in the paper. By a Cole-Hopf type transformation, the singular chemotaxis is converted into a non-singular hyperbolic system. Then we study the transformed system and establish the global existence, asymptotic decay rates and diffusion convergence rate of solutions by the method of energy estimates. The main novelty of our results is the finding of a hidden interactive dissipation structure in the system by which the energy dissipation is established.
Original languageEnglish
Pages (from-to)2225-2258
Number of pages34
JournalJournal of Differential Equations
Volume260
Issue number3
DOIs
Publication statusPublished - 5 Feb 2016

Keywords

  • Chemotaxis
  • Decay estimates
  • Energy estimates
  • Global well-posedness
  • Tumor angiogenesis

ASJC Scopus subject areas

  • Analysis

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