Boundedness in a two-dimensional chemotaxis system with signal-dependent motility and indirect signal consumption
Abstract
In this paper, we consider the following chemotaxis system with signal-dependent motility and indirect signal consumption: {ut=Δ(D(u)ϕ(v))+ρu(1−ul−1),(x,t)∈Ω×(0,∞),vt=Δv−vw,(x,t)∈Ω×(0,∞),wt=−δw+u,(x,t)∈Ω×(0,∞),under the smooth bounded domain Ω⊂R2 with homogeneous Neumann boundary conditions, where the nonlinearities D(u)=(u+1)m with m>0 and the motility function ϕ satisfies the condition: ϕ∈C3((0,∞)) is positive on [0,∞). It is proved that the system possesses a unique global classical solution that is uniformly bounded. Moreover, if ρ>0, the asymptotic behavior of the solution is discussed.
Fields of Study & Subjects
Mathematical Biology Tumor Growth
Mathematical and Theoretical Epidemiology and Ecology Models
Nonlinear Partial Differential Equations
Publication details
- Journal / source
- Applicable Analysis
- Volume
- 105
- Issue
- 12
- Pages
- 2708–2722
- Publication date
- 3 February 2026
- Language
- EN