Results 1 to 10 of about 895 (106)
Demonstratio Mathematica, 2021 Keller-Segel chemotaxis model is described by a system of nonlinear partial differential equations: a convection diffusion equation for the cell density coupled with a reaction-diffusion equation for chemoattractant concentration.
Slimani Ali +2 more
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Classical solutions to Cauchy problems for parabolic–elliptic systems of Keller-Segel type
Open Mathematics, 2023 The Cauchy problem in Rn{{\mathbb{R}}}^{n}, n≥2n\ge 2, for ut=Δu−∇⋅(uS⋅∇v),0=Δv+u,(⋆)\begin{array}{r}\left\{\phantom{\rule[-1.25em]{}{0ex}}\begin{array}{l}{u}_{t}=\Delta u-\nabla \cdot \left(uS\cdot \nabla v),\\ 0=\Delta v+u,\end{array}\right.\hspace{2 ...
Winkler Michael
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Advances in Nonlinear Analysis, 2022 In this article, we will develop an analytical approach to construct the global bounded weak solutions to the initial-boundary value problem of a three-dimensional chemotaxis-Stokes system with porous medium cell diffusion Δnm\Delta {n}^{m} for m≥6563m ...
Tian Yu, Xiang Zhaoyin
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Global existence and boundedness in a two-species chemotaxis system with nonlinear diffusion
Open Mathematics, 2021 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
Huang Ting, Hou Zhibo, Han Yongjie
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Advances in Nonlinear Analysis, 2021 We consider a degenerate chemotaxis model with two-species and two-stimuli in dimension d ≥ 3 and find two critical curves intersecting at one point which separate the global existence and blow up of weak solutions to the problem.
Carrillo Antonio José, Lin Ke
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Chemotaxis(-fluid) systems with logarithmic sensitivity and slow consumption: global generalized solutions and eventual smoothness [PDF]
, 2022 We consider the system \begin{align*} \begin{cases} n_t + u \cdot \nabla n = \Delta n - \chi \nabla \cdot (\frac{n}{c} \nabla c),
arxiv +1 more source
Advanced Nonlinear Studies, 2022 The chemotaxis–Stokes system nt+u⋅∇n=∇⋅(D(n)∇n)−∇⋅(nS(x,n,c)⋅∇c),ct+u⋅∇c=Δc−nc,ut=Δu+∇P+n∇Φ,∇⋅u=0,\left\{\begin{array}{l}{n}_{t}+u\cdot \nabla n=\nabla \cdot (D\left(n)\nabla n)-\nabla \cdot (nS\left(x,n,c)\cdot \nabla c),\\ {c}_{t}+u\cdot \nabla c ...
Winkler Michael
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The fractional Keller-Segel model [PDF]
, 2006 The Keller-Segel model is a system of partial differential equations modelling chemotactic aggregation in cellular systems. This model has blowing up solutions for large enough initial conditions in dimensions d >= 2, but all the solutions are regular in
Brenner M P +9 more
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Boundary layer analysis for a 2-D Keller-Segel model
Open Mathematics, 2020 We study the boundary layer problem of a Keller-Segel model in a domain of two space dimensions with vanishing chemical diffusion coefficient. By using the method of matched asymptotic expansions of singular perturbation theory, we construct an accurate ...
Meng Linlin, Xu Wen-Qing, Wang Shu
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LOCAL-IN-TIME SOLVABILITY OF TARGET DETECTION MODEL IN MOLECULAR COMMUNICATION NETWORK
International Journal of Apllied Mathematics, 2018 This paper is concerned with a model of the target detection that is actively discussed in the study of molecular communication network these days. We first verify the solvability of the stationary problem, and then the existence of a strong local-in ...
H. Honda
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