Boundedness in a quasilinear attraction–repulsion chemotaxis system with nonlinear sensitivity and logistic source
Abstract In this paper, we deal with the following quasilinear attraction–repulsion model: {ut=∇⋅(D(u)∇u)−∇⋅(S(u)χ(v)∇v)+∇⋅(F(u)ξ(w)∇w)+f(u),x∈Ω,t>0,vt=Δv+βu−αv,x∈Ω,t>0,0=Δw+γu−δw,x∈Ω,t>0,u(x,0)=u0(x),v(x,0)=v0(x),x∈Ω $$ \textstyle\begin{cases} u_{t}=\nabla \cdot (D(u)\nabla u)-\nabla \cdot...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2019-07-01
|
| Series: | Boundary Value Problems |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1186/s13661-019-1232-y |
| _version_ | 1817983404852903936 |
|---|---|
| author | Lijun Yan Zuodong Yang |
| author_facet | Lijun Yan Zuodong Yang |
| author_sort | Lijun Yan |
| collection | DOAJ |
| description | Abstract In this paper, we deal with the following quasilinear attraction–repulsion model: {ut=∇⋅(D(u)∇u)−∇⋅(S(u)χ(v)∇v)+∇⋅(F(u)ξ(w)∇w)+f(u),x∈Ω,t>0,vt=Δv+βu−αv,x∈Ω,t>0,0=Δw+γu−δw,x∈Ω,t>0,u(x,0)=u0(x),v(x,0)=v0(x),x∈Ω $$ \textstyle\begin{cases} u_{t}=\nabla \cdot (D(u)\nabla u)-\nabla \cdot ( S(u)\chi (v)\nabla v)+ \nabla \cdot ( F(u)\xi (w)\nabla w)+f(u), &x\in \varOmega , t>0, \\ v_{t}=\Delta v+\beta u-\alpha v, &x\in \varOmega ,t>0, \\ 0=\Delta w+\gamma u-\delta w, &x\in \varOmega , t>0, \\ u(x,0)=u_{0}(x), \quad\quad v(x,0)= v_{0}(x), &x\in \varOmega \end{cases} $$ with homogeneous Neumann boundary conditions in a smooth bounded domain Ω⊂Rn $\varOmega \subset R^{n}$ ( n≥2 $n\geq 2$). Let the chemotactic sensitivity χ(v) $\chi (v)$ be a positive constant, and let the chemotactic sensitivity ξ(w) $\xi (w)$ be a nonlinear function. Under some assumptions, we prove that the system has a unique globally bounded classical solution. |
| first_indexed | 2024-04-13T23:32:41Z |
| format | Article |
| id | doaj.art-b082bdffebac4f28b6400558b207b651 |
| institution | Directory Open Access Journal |
| issn | 1687-2770 |
| language | English |
| last_indexed | 2024-04-13T23:32:41Z |
| publishDate | 2019-07-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Boundary Value Problems |
| spelling | doaj.art-b082bdffebac4f28b6400558b207b6512022-12-22T02:24:51ZengSpringerOpenBoundary Value Problems1687-27702019-07-012019111310.1186/s13661-019-1232-yBoundedness in a quasilinear attraction–repulsion chemotaxis system with nonlinear sensitivity and logistic sourceLijun Yan0Zuodong Yang1School of Science, North China Institute of Science and TechnologySchool of Teacher Education, Nanjing Normal UniversityAbstract In this paper, we deal with the following quasilinear attraction–repulsion model: {ut=∇⋅(D(u)∇u)−∇⋅(S(u)χ(v)∇v)+∇⋅(F(u)ξ(w)∇w)+f(u),x∈Ω,t>0,vt=Δv+βu−αv,x∈Ω,t>0,0=Δw+γu−δw,x∈Ω,t>0,u(x,0)=u0(x),v(x,0)=v0(x),x∈Ω $$ \textstyle\begin{cases} u_{t}=\nabla \cdot (D(u)\nabla u)-\nabla \cdot ( S(u)\chi (v)\nabla v)+ \nabla \cdot ( F(u)\xi (w)\nabla w)+f(u), &x\in \varOmega , t>0, \\ v_{t}=\Delta v+\beta u-\alpha v, &x\in \varOmega ,t>0, \\ 0=\Delta w+\gamma u-\delta w, &x\in \varOmega , t>0, \\ u(x,0)=u_{0}(x), \quad\quad v(x,0)= v_{0}(x), &x\in \varOmega \end{cases} $$ with homogeneous Neumann boundary conditions in a smooth bounded domain Ω⊂Rn $\varOmega \subset R^{n}$ ( n≥2 $n\geq 2$). Let the chemotactic sensitivity χ(v) $\chi (v)$ be a positive constant, and let the chemotactic sensitivity ξ(w) $\xi (w)$ be a nonlinear function. Under some assumptions, we prove that the system has a unique globally bounded classical solution.http://link.springer.com/article/10.1186/s13661-019-1232-yAttraction–repulsionBoundednessNonlinear sensitivityLogistic source |
| spellingShingle | Lijun Yan Zuodong Yang Boundedness in a quasilinear attraction–repulsion chemotaxis system with nonlinear sensitivity and logistic source Boundary Value Problems Attraction–repulsion Boundedness Nonlinear sensitivity Logistic source |
| title | Boundedness in a quasilinear attraction–repulsion chemotaxis system with nonlinear sensitivity and logistic source |
| title_full | Boundedness in a quasilinear attraction–repulsion chemotaxis system with nonlinear sensitivity and logistic source |
| title_fullStr | Boundedness in a quasilinear attraction–repulsion chemotaxis system with nonlinear sensitivity and logistic source |
| title_full_unstemmed | Boundedness in a quasilinear attraction–repulsion chemotaxis system with nonlinear sensitivity and logistic source |
| title_short | Boundedness in a quasilinear attraction–repulsion chemotaxis system with nonlinear sensitivity and logistic source |
| title_sort | boundedness in a quasilinear attraction repulsion chemotaxis system with nonlinear sensitivity and logistic source |
| topic | Attraction–repulsion Boundedness Nonlinear sensitivity Logistic source |
| url | http://link.springer.com/article/10.1186/s13661-019-1232-y |
| work_keys_str_mv | AT lijunyan boundednessinaquasilinearattractionrepulsionchemotaxissystemwithnonlinearsensitivityandlogisticsource AT zuodongyang boundednessinaquasilinearattractionrepulsionchemotaxissystemwithnonlinearsensitivityandlogisticsource |