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Michael Winkler 《Journal of Mathematical Analysis and Applications》2008,348(2):708-729
We consider the chemotaxis system
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Global existence and boundedness of classical solutions for a chemotaxis model with consumption of chemoattractant and logistic source 下载免费PDF全文
This paper deals with the following chemotaxis system: under homogeneous Neumann boundary conditions in a bounded domain with smooth boundary. Here, δ and χ are some positive constants and f is a smooth function that satisfies with some constants a ?0,b > 0, and γ > 1. We prove that the classical solutions to the preceding system are global and bounded provided that Copyright © 2016 John Wiley & Sons, Ltd. 相似文献
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《Mathematical Methods in the Applied Sciences》2018,41(5):1809-1824
In this paper, we study the zero‐flux chemotaxis‐system where Ω is a bounded and smooth domain of , n≥1, and where , k,μ>0 and α≤1. For any v≥0, the chemotactic sensitivity function is assumed to behave as the prototype χ(v)=χ0/(1+av)2, with a≥0 and χ0>0. We prove that for any nonnegative and sufficiently regular initial data u(x,0), the corresponding initial‐boundary value problem admits a unique global bounded classical solution if α<1; indeed, for α=1, the same conclusion is obtained provided μ is large enough. Finally, we illustrate the range of dynamics present within the chemotaxis system in 1, 2, and 3 dimensions by means of numerical simulations. 相似文献
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《Mathematische Nachrichten》2018,291(14-15):2318-2333
In this paper we study the zero‐flux chemotaxis‐system Ω being a convex smooth and bounded domain of , , and where , and . For any the chemotactic sensitivity function is assumed to behave as the prototype , with and . We prove that for nonnegative and sufficiently regular initial data and , the corresponding initial‐boundary value problem admits a unique globally bounded classical solution provided μ is large enough. 相似文献
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Global existence of solutions for a fully parabolic chemotaxis system with consumption of chemoattractant and logistic source 下载免费PDF全文
This paper deals with a fully parabolic chemotaxis system with consumption of chemoattractant and logistic source under homogeneous Neumann boundary conditions in a smooth bounded domain . The functions χ and f are assumed to generalize the chemotactic sensitivity function and logistic source respectively. Under some conditions, we obtain that the corresponding initial‐boundary value problem possesses a unique global classical solution that is uniformly bounded. 相似文献
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Chunyan Ji Daqing Jiang Ningzhong Shi Donal O'Regan 《Mathematical Methods in the Applied Sciences》2007,30(1):77-89
This paper discusses a randomized logistic equation (1) with initial value x(0)=x0>0, where B(t) is a standard one‐dimension Brownian motion, and θ∈(0, 0.5). We show that the positive solution of the stochastic differential equation does not explode at any finite time under certain conditions. In addition, we study the existence, uniqueness, boundedness, stochastic persistence and global stability of the positive solution. Copyright © 2006 John Wiley & Sons, Ltd. 相似文献