Global Solutions in the Species Competitive Chemotaxis System with Inequal Diffusion Rates

Huaihuo Cao

Discrete Dynamics in Nature and Society, 2016, vol. 2016, issue 1

Abstract: This paper is devoted to studying the two‐species competitive chemotaxis system with signal‐dependent chemotactic sensitivities and inequal diffusion rates u1t = Δu1 − ∇·(u1χ1(v)∇v) + μ1u1(1 − u1 − a1u2), x ∈ Ω, t > 0, u2t = Δu2 − ∇·(u2χ2(v)∇v) + μ2u2(1 − a2u1 − u2), x ∈ Ω, t > 0, vt = τΔv − γv + u1 + u2, x ∈ Ω, t > 0, under homogeneous Neumann boundary conditions in a bounded and regular domain Ω⊂Rn (n≥1). If the nonnegative initial date (u10,u20,v0)∈(C1(Ω¯)) 3 and v0∈(v_,v¯) where the constants v¯>v_≥0, the system possesses a unique global solution that is uniformly bounded under some suitable assumptions on the chemotaxis sensitivity functions χ1(v), χ2(v) and linear chemical production function −γv + u1 + u2.

Date: 2016
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https://doi.org/10.1155/2016/5015246

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnddns:v:2016:y:2016:i:1:n:5015246

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