To the exclusion of blow-up in a three-dimensional chemotaxis-growth model with indirect attractant production
Abstract
This work considers the chemotaxis-growth system
In striking contrast to the corresponding three-dimensional two-component chemo-taxis-growth system to which the global existence or blow-up of classical solutions largely remains open when μ>0 is small, it is shown that whenever μ>0,τ>0 and δ>0, for any given non-negative and suitably smooth initial data (u0,v0,w0) satisfying u0≢0, the system (⋆) admits a unique global classical solution that is uniformly-in-time bounded, which rules out the possibility of blow-up of solutions in finite time or in infinite time.
Moreover, under the fully explicit condition μ>18δ2 the solution (u,v,w) exponentially converges to the constant stationary solution (1,1δ,1δ) in the norm of L∞(Ω) as t→∞.
Communicated by M. Winkler
