Global existence and boundedness in a two-species chemotaxis system with nonlinear diffusion

This paper is concerned with a chemotaxis system ut=Δum−∇⋅(χ1(w)u∇w)+μ1u(1−u−a1v),x∈Ω,t>0,vt=Δvn−∇⋅(χ2(w)v∇w)+μ2v(1−a2u−v),x∈Ω,t>0,wt=Δw−(αu+βv)w,x∈Ω,t>0,\left\{\begin{array}{ll}{u}_{t}=\Delta {u}^{m}-\nabla \cdot \left({\chi }_{1}\left(w)u\nabla w)+{\mu }_{1}u\left(1-u-{a}_{1}v),& x\in...

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Autores principales:	Huang Ting, Hou Zhibo, Han Yongjie
Formato:	article
Lenguaje:	EN
Publicado:	De Gruyter 2021
Materias:	chemotaxis system nonlinear diffusion boundedness logistic source 92c17 35k55 35q92 Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/8f7f0d0f60334a418775b4ee09dc11c5
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spelling	oai:doaj.org-article:8f7f0d0f60334a418775b4ee09dc11c52021-12-05T14:10:53ZGlobal existence and boundedness in a two-species chemotaxis system with nonlinear diffusion2391-545510.1515/math-2021-0074https://doaj.org/article/8f7f0d0f60334a418775b4ee09dc11c52021-08-01T00:00:00Zhttps://doi.org/10.1515/math-2021-0074https://doaj.org/toc/2391-5455This paper is concerned with a chemotaxis system ut=Δum−∇⋅(χ1(w)u∇w)+μ1u(1−u−a1v),x∈Ω,t>0,vt=Δvn−∇⋅(χ2(w)v∇w)+μ2v(1−a2u−v),x∈Ω,t>0,wt=Δw−(αu+βv)w,x∈Ω,t>0,\left\{\begin{array}{ll}{u}_{t}=\Delta {u}^{m}-\nabla \cdot \left({\chi }_{1}\left(w)u\nabla w)+{\mu }_{1}u\left(1-u-{a}_{1}v),& x\in \Omega ,\hspace{0.33em}t\gt 0,\\ {v}_{t}=\Delta {v}^{n}-\nabla \cdot \left({\chi }_{2}\left(w)v\nabla w)+{\mu }_{2}v\left(1-{a}_{2}u-v),& x\in \Omega ,\hspace{0.33em}t\gt 0,\\ {w}_{t}=\Delta w-\left(\alpha u+\beta v)w,& x\in \Omega ,\hspace{0.33em}t\gt 0,\end{array}\right. under homogeneous Neumann boundary conditions in a bounded domain Ω⊂R3\Omega \subset {{\mathbb{R}}}^{3} with smooth boundary, where μ1,μ2>0{\mu }_{1},{\mu }_{2}\gt 0, a1,a2>0{a}_{1},{a}_{2}\gt 0, α,β>0\alpha ,\beta \gt 0, and the chemotactic sensitivity function χi∈C1([0,∞)){\chi }_{i}\in {C}^{1}({[}0,\infty )), χi′≥0{\chi }_{i}^{^{\prime} }\ge 0. It is proved that for any large initial data, for any m,n>1m,n\gt 1, the system admits a global weak solution, which is uniformly bounded.Huang TingHou ZhiboHan YongjieDe Gruyterarticlechemotaxis systemnonlinear diffusionboundednesslogistic source92c1735k5535q92MathematicsQA1-939ENOpen Mathematics, Vol 19, Iss 1, Pp 949-962 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	chemotaxis system nonlinear diffusion boundedness logistic source 92c17 35k55 35q92 Mathematics QA1-939
spellingShingle	chemotaxis system nonlinear diffusion boundedness logistic source 92c17 35k55 35q92 Mathematics QA1-939 Huang Ting Hou Zhibo Han Yongjie Global existence and boundedness in a two-species chemotaxis system with nonlinear diffusion
description	This paper is concerned with a chemotaxis system ut=Δum−∇⋅(χ1(w)u∇w)+μ1u(1−u−a1v),x∈Ω,t>0,vt=Δvn−∇⋅(χ2(w)v∇w)+μ2v(1−a2u−v),x∈Ω,t>0,wt=Δw−(αu+βv)w,x∈Ω,t>0,\left\{\begin{array}{ll}{u}_{t}=\Delta {u}^{m}-\nabla \cdot \left({\chi }_{1}\left(w)u\nabla w)+{\mu }_{1}u\left(1-u-{a}_{1}v),& x\in \Omega ,\hspace{0.33em}t\gt 0,\\ {v}_{t}=\Delta {v}^{n}-\nabla \cdot \left({\chi }_{2}\left(w)v\nabla w)+{\mu }_{2}v\left(1-{a}_{2}u-v),& x\in \Omega ,\hspace{0.33em}t\gt 0,\\ {w}_{t}=\Delta w-\left(\alpha u+\beta v)w,& x\in \Omega ,\hspace{0.33em}t\gt 0,\end{array}\right. under homogeneous Neumann boundary conditions in a bounded domain Ω⊂R3\Omega \subset {{\mathbb{R}}}^{3} with smooth boundary, where μ1,μ2>0{\mu }_{1},{\mu }_{2}\gt 0, a1,a2>0{a}_{1},{a}_{2}\gt 0, α,β>0\alpha ,\beta \gt 0, and the chemotactic sensitivity function χi∈C1([0,∞)){\chi }_{i}\in {C}^{1}({[}0,\infty )), χi′≥0{\chi }_{i}^{^{\prime} }\ge 0. It is proved that for any large initial data, for any m,n>1m,n\gt 1, the system admits a global weak solution, which is uniformly bounded.
format	article
author	Huang Ting Hou Zhibo Han Yongjie
author_facet	Huang Ting Hou Zhibo Han Yongjie
author_sort	Huang Ting
title	Global existence and boundedness in a two-species chemotaxis system with nonlinear diffusion
title_short	Global existence and boundedness in a two-species chemotaxis system with nonlinear diffusion
title_full	Global existence and boundedness in a two-species chemotaxis system with nonlinear diffusion
title_fullStr	Global existence and boundedness in a two-species chemotaxis system with nonlinear diffusion
title_full_unstemmed	Global existence and boundedness in a two-species chemotaxis system with nonlinear diffusion
title_sort	global existence and boundedness in a two-species chemotaxis system with nonlinear diffusion
publisher	De Gruyter
publishDate	2021
url	https://doaj.org/article/8f7f0d0f60334a418775b4ee09dc11c5
work_keys_str_mv	AT huangting globalexistenceandboundednessinatwospecieschemotaxissystemwithnonlineardiffusion AT houzhibo globalexistenceandboundednessinatwospecieschemotaxissystemwithnonlineardiffusion AT hanyongjie globalexistenceandboundednessinatwospecieschemotaxissystemwithnonlineardiffusion
_version_	1718371615877627904

Global existence and boundedness in a two-species chemotaxis system with nonlinear diffusion

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