Global Solutions in the Species Competitive Chemotaxis System with Inequal Diffusion Rates
This paper is devoted to studying the two-species competitive chemotaxis system with signal-dependent chemotactic sensitivities and inequal diffusion rates u1t=Δu1-∇·u1χ1v∇v+μ1u11-u1-a1u2, x∈Ω, t>0, u2t=Δu2-∇·u2χ2v∇v+μ2u21-a2u1-u2, x∈Ω, t>0, vt=τΔv-γv+u1+u2, x∈Ω, t>0, under homogeneous N...
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2016-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2016/5015246 |
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| Summary: | This paper is devoted to studying the two-species competitive chemotaxis system with signal-dependent chemotactic sensitivities and inequal diffusion rates u1t=Δu1-∇·u1χ1v∇v+μ1u11-u1-a1u2, x∈Ω, t>0, u2t=Δu2-∇·u2χ2v∇v+μ2u21-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. |
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| ISSN: | 1026-0226 1607-887X |