Global boundedness and asymptotic behavior of the chemotaxis system for alopecia areata with singular sensitivity
This paper is concerned with a three-component chemotaxis system for alopecia areata with singular sensitivity ut=Δu−χ1∇⋅uw∇w+w−μ1u2,x∈Ω,t>0,vt=Δv−χ2∇⋅vw∇w+w+ruv−μ2v2,x∈Ω,t>0,wt=Δw+u+v−w,x∈Ω,t>0,∂u∂ν=∂v∂ν=∂w∂ν=0,x∈∂Ω,t>0,u(x,0)=u0(x),v(x,0)=v0(x),w(x,0)=w0(x),x∈Ωunder the homogeneous Neu...
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| Format: | Article |
| Language: | English |
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Elsevier
2024-05-01
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| Series: | Results in Applied Mathematics |
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| Online Access: | http://www.sciencedirect.com/science/article/pii/S2590037424000207 |
| _version_ | 1797220257895546880 |
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| author | Peng Gao Lu Xu |
| author_facet | Peng Gao Lu Xu |
| author_sort | Peng Gao |
| collection | DOAJ |
| description | This paper is concerned with a three-component chemotaxis system for alopecia areata with singular sensitivity ut=Δu−χ1∇⋅uw∇w+w−μ1u2,x∈Ω,t>0,vt=Δv−χ2∇⋅vw∇w+w+ruv−μ2v2,x∈Ω,t>0,wt=Δw+u+v−w,x∈Ω,t>0,∂u∂ν=∂v∂ν=∂w∂ν=0,x∈∂Ω,t>0,u(x,0)=u0(x),v(x,0)=v0(x),w(x,0)=w0(x),x∈Ωunder the homogeneous Neumann boundary conditions in a smoothly bounded domain Ω⊂R2, where the parameters χi, μi (i=1,2) and r are positive. It is showed that if χ1,χ2<52, this system admits a globally bounded classical solution. Furthermore, under the particular conditions of μ1<μ2<3μ1 and r=μ2−μ1, the global bounded solution converges to the steady state (2μ1,2μ1,4μ1) as t→∞. |
| first_indexed | 2024-04-24T12:46:40Z |
| format | Article |
| id | doaj.art-4e200db6c34d4cb4b24145f121ecef33 |
| institution | Directory Open Access Journal |
| issn | 2590-0374 |
| language | English |
| last_indexed | 2024-04-24T12:46:40Z |
| publishDate | 2024-05-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Results in Applied Mathematics |
| spelling | doaj.art-4e200db6c34d4cb4b24145f121ecef332024-04-07T04:36:12ZengElsevierResults in Applied Mathematics2590-03742024-05-0122100450Global boundedness and asymptotic behavior of the chemotaxis system for alopecia areata with singular sensitivityPeng Gao0Lu Xu1College of Mathematics and Statistics, Yili Normal University, Yining 835000, PR ChinaCollege of Mathematics and Statistics, Yili Normal University, Yining 835000, PR China; Institute of Applied Mathematics, Yili Normal University, Yining 835000, PR China; Corresponding author at: College of Mathematics and Statistics, Yili Normal University, Yining 835000, PR China.This paper is concerned with a three-component chemotaxis system for alopecia areata with singular sensitivity ut=Δu−χ1∇⋅uw∇w+w−μ1u2,x∈Ω,t>0,vt=Δv−χ2∇⋅vw∇w+w+ruv−μ2v2,x∈Ω,t>0,wt=Δw+u+v−w,x∈Ω,t>0,∂u∂ν=∂v∂ν=∂w∂ν=0,x∈∂Ω,t>0,u(x,0)=u0(x),v(x,0)=v0(x),w(x,0)=w0(x),x∈Ωunder the homogeneous Neumann boundary conditions in a smoothly bounded domain Ω⊂R2, where the parameters χi, μi (i=1,2) and r are positive. It is showed that if χ1,χ2<52, this system admits a globally bounded classical solution. Furthermore, under the particular conditions of μ1<μ2<3μ1 and r=μ2−μ1, the global bounded solution converges to the steady state (2μ1,2μ1,4μ1) as t→∞.http://www.sciencedirect.com/science/article/pii/S2590037424000207ChemotaxisSingular sensitivityBoundednessAsymptotic behavior |
| spellingShingle | Peng Gao Lu Xu Global boundedness and asymptotic behavior of the chemotaxis system for alopecia areata with singular sensitivity Results in Applied Mathematics Chemotaxis Singular sensitivity Boundedness Asymptotic behavior |
| title | Global boundedness and asymptotic behavior of the chemotaxis system for alopecia areata with singular sensitivity |
| title_full | Global boundedness and asymptotic behavior of the chemotaxis system for alopecia areata with singular sensitivity |
| title_fullStr | Global boundedness and asymptotic behavior of the chemotaxis system for alopecia areata with singular sensitivity |
| title_full_unstemmed | Global boundedness and asymptotic behavior of the chemotaxis system for alopecia areata with singular sensitivity |
| title_short | Global boundedness and asymptotic behavior of the chemotaxis system for alopecia areata with singular sensitivity |
| title_sort | global boundedness and asymptotic behavior of the chemotaxis system for alopecia areata with singular sensitivity |
| topic | Chemotaxis Singular sensitivity Boundedness Asymptotic behavior |
| url | http://www.sciencedirect.com/science/article/pii/S2590037424000207 |
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