Long time asymptotics of small mass solutions for a chemotaxis-consumption system involving prescribed signal concentrations on the boundary

Soo Oh Yang, Jaewook Ahn

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

Abstract

This paper investigates a parabolic–elliptic chemotaxis-consumption system with signal dependent sensitivity χ=χ(c) under no-flux/Dirichlet boundary conditions. For general χ which may allow singularities at c=0, the global existence and boundedness of radial large data solutions are established in dimensions d≥2. In particular, when χ(c)=1, we also find that the constructed solution converges asymptotically to a nonhomogeneous steady state if the initial mass is small. On the other hand, for the system with χ(c)=c, a Lyapunov-type inequality is derived. This inequality not only leads to a result on global existence of smooth solutions with non-radial large data in two dimensions but moreover, provides long-time asymptotics of non-radial (d=2) and radial (d≥2) solutions at suitably small mass levels.

Original languageEnglish
Article number104129
JournalNonlinear Analysis: Real World Applications
Volume79
DOIs
StatePublished - Oct 2024

Keywords

  • Chemotaxis
  • Global existence
  • Long time behaviors

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