Abstract
The paper is concerned with the following chemotaxis system with nonlinear motility functions (equation presented) subject to homogeneous Neumann boundary conditions in a bounded domain Ω⊂ R2 with smooth boundary, where the motility functions γ(v) and χ(v) satisfy the following conditions • (γ; χ) 2 [C2[0;1)]2 with (v) >0 and jχ(v)j2 γ(v) is bounded for all v ≥ 0. By employing the method of energy estimates, we establish the existence of globally bounded solutions of (*) with μ >0 for any u0 ∈ W1;1() with u0 ≥ (≢)0. Then based on a Lyapunov function, we show that all solutions (u; v) of (*) will exponentially converge to the unique constant steady state (1; 1) provided μ>K0 16 with K0 = max 0≤v≤1 Jχ(v)j2 γ(v) .
Original language | English |
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Pages (from-to) | 3023-3041 |
Number of pages | 19 |
Journal | Discrete and Continuous Dynamical Systems - Series B |
Volume | 26 |
Issue number | 6 |
DOIs | |
Publication status | Published - Jun 2021 |
ASJC Scopus subject areas
- Discrete Mathematics and Combinatorics
- Applied Mathematics