Global boundedness for an indirect consumption chemotaxis model with signal-dependent motility

IF 1.2 3区 数学 Q1 MATHEMATICS
Chun Wu
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引用次数: 0

Abstract

In this paper, we consider the following chemotaxis system with signal-dependent motility and indirect signal consumption{ut=Δ(D(u)ϕ(v)),(x,t)Ω×(0,),vt=Δvvw,(x,t)Ω×(0,),wt=Δww+u,(x,t)Ω×(0,), under the smooth bounded domain ΩRn(n3) with homogeneous Neumann boundary conditions, where the nonlinearities D(u) and the motility function ϕ satisfy the following conditionD(u)=(u+a)mandϕC1([0,))is positive on[0,). It has been demonstrated that, for any sufficiently regular initial data, the associated initial-boundary value problem allows for global classical solutions. Moreover, the asymptotic behavior of the solutions is analyzed and studied.
具有信号依赖运动的间接消耗趋化模型的全局有界性
在本文中,我们考虑以下具有信号依赖运动和间接信号消耗的趋化系统{ut=Δ(D(u)ϕ(v)),(x,t)∈Ω×(0,∞),vt=Δv−vw,(x,t)∈Ω×(0,∞),wt=Δw−w+u,(x,t)∈Ω×(0,∞),在光滑有界域Ω∧Rn(n≤3)下具有齐次Neumann边界条件,其中非线性D(u)和运动函数φ满足以下条件ond (u)=(u+a) mandφ∈C1([0,∞))在[0,∞)上为正。已经证明,对于任何足够正则的初始数据,相关的初始边值问题允许全局经典解。此外,还分析和研究了解的渐近性态。
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来源期刊
CiteScore
2.50
自引率
7.70%
发文量
790
审稿时长
6 months
期刊介绍: The Journal of Mathematical Analysis and Applications presents papers that treat mathematical analysis and its numerous applications. The journal emphasizes articles devoted to the mathematical treatment of questions arising in physics, chemistry, biology, and engineering, particularly those that stress analytical aspects and novel problems and their solutions. Papers are sought which employ one or more of the following areas of classical analysis: • Analytic number theory • Functional analysis and operator theory • Real and harmonic analysis • Complex analysis • Numerical analysis • Applied mathematics • Partial differential equations • Dynamical systems • Control and Optimization • Probability • Mathematical biology • Combinatorics • Mathematical physics.
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