Regular solutions of chemotaxis-consumption systems involving tensor-valued sensitivities and Robin type boundary conditions

Jaewook Ahn, Kyungkeun Kang, Jihoon Lee

Research output: Contribution to journalArticlepeer-review

4 Scopus citations

Abstract

This paper deals with a parabolic-elliptic chemotaxis-consumption system with tensor-valued sensitivity S(x,n,c) under no-flux boundary conditions for n and Robin-type boundary conditions for c. The global existence of bounded classical solutions is established in dimension two under general assumptions on tensor-valued sensitivity S. One of the main steps is to show that ∇c(·, t) becomes tiny in L2(Br(x) ∩ ω¯) for every x ω¯ and t when r is sufficiently small, which seems to be of independent interest. On the other hand, in the case of scalar-valued sensitivity S = χ(x,n,c)I, there exists a bounded classical solution globally in time for two and higher dimensions provided the domain is a ball with radius R and all given data are radial. The result of the radial case covers scalar-valued sensitivity χ that can be singular at c = 0.

Original languageEnglish
Pages (from-to)2337-2360
Number of pages24
JournalMathematical Models and Methods in Applied Sciences
Volume33
Issue number11
DOIs
StatePublished - 1 Oct 2023

Keywords

  • Chemotaxis-consumption system
  • regular solution
  • Robin-type boundary condition
  • tensor-valued sensitivity

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