Asymptotic profile of a parabolic-hyperbolic system with boundary effect arising from tumor angiogenesis

Ming Mei, Hongyun Peng, Zhian Wang

Research output: Journal article publicationJournal articleAcademic researchpeer-review

11 Citations (Scopus)

Abstract

This paper concerns a parabolic-hyperbolic system on the half space R+ with boundary effect. The system is derived from a singular chemotaxis model describing the initiation of tumor angiogenesis. We show that the solution of the system subject to appropriate boundary conditions converges to a traveling wave profile as time tends to infinity if the initial data is a small perturbation around the wave which is shifted far away from the boundary but its amplitude can be arbitrarily large.
Original languageEnglish
Pages (from-to)5168-5191
Number of pages24
JournalJournal of Differential Equations
Volume259
Issue number10
DOIs
Publication statusPublished - 1 Jan 2015

Keywords

  • Asymptotic stability
  • Boundary effect
  • Chemotaxis
  • Energy estimates
  • Traveling wave solutions

ASJC Scopus subject areas

  • Analysis

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