Dynamics in a Chemotaxis Model with Periodic Source (original) (raw)
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Global existence and boundedness of classical solutions for a chemotaxis model with logistic source
Comptes Rendus Mathematique, 2013
This work is concerned with a chemotactic model for the dynamics of social interactions between two species-foragers u and exploiters v, as well as the dynamics of food resources w consumed by these two species. The foragers search for food directly, while the exploiters head for food by following the foragers. Specifically, the parabolic system in a smoothly bounded convex n-dimensional domain Ω , { ut = ∆u − ∇ • (S 1 (u)∇w), x ∈ Ω , t > 0, vt = ∆v − ∇ • (S 2 (v)∇u), x ∈ Ω , t > 0, wt = d∆w − λ(u + v)w − µw + r(x, t), x ∈ Ω , t > 0, is considered for the constants d, λ, µ > 0 and r ∈ C 0 (Ω × [0, ∞)) with a uniform bound. Volume-filling effects account for a simple version by taking S 1 (u) = u(1 − u), S 2 (v) = v(1 − v). We prove the global existence and boundedness of the unique classical solution to this forager-exploiter model associated with no-flux boundary conditions under the mild assumption that the initial data u 0 , v 0 , w 0 satisfy 0 ≤ u 0 , v 0 ≤ 1 and w 0 ≥ 0.