共查询到20条相似文献,搜索用时 15 毫秒
1.
Global existence and blow-up for the solutions to nonlinear parabolic-elliptic system modelling chemotaxis 总被引:1,自引:0,他引:1
In this paper we study the global in-time and blow-up solutionsfor the simplified KellerSegel system modelling chemotaxis.We prove that there is a critical number which determines theoccurrence of blowup in the two-dimensional case for 1 <p < 2. In three- or higher-dimensional cases, we show thatthe radial symmetrical solution will blow up if 1 < p <N/N2 (N 3) for non-negative initial value. 相似文献
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Venkatasubramaniam Bhuvaneswari Lingeshwaran Shangerganesh Krishnan Balachandran 《Mathematical Methods in the Applied Sciences》2015,38(17):3738-3746
In this paper, we study the global existence of solution for the quasilinear chemotaxis system with Dirichlet boundary conditions, and further we show that the blow up properties of the solution depend only on the first eigenvalue. Copyright © 2014 John Wiley & Sons, Ltd. 相似文献
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On Existence of Local Solutions for a Hyperbolic System Modelling Chemotaxis with Memory Term 下载免费PDF全文
Shaohua Wu & Pengfei Wang 《偏微分方程(英文版)》2021,34(2):170-185
In this paper, we discuss the local existence of weak solutions for some hyperbolic parabolic systems modelling chemotaxis with memory term.The main methods we use are the fixed point theorem and semigroup theory. 相似文献
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We establish an existence result for strongly indefinite semilinear elliptic systems with Neumann boundary condition, and we study the limiting behavior of the positive solutions of the singularly perturbed problem. 相似文献
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对带两个趋化性参数的趋化性模型平衡解的存在性问题进行研究.在参数满足特定的条件下,应用局部分岔理论得到非常数平衡解的局部分岔结构,从而证明了该趋化性模型存在无穷多个非常数正平衡解. 相似文献
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** Email: d.j.needham{at}reading.ac.uk We consider generalization of the theory for the evolution ofreactiondiffusion and accelerating wavefronts in KPP-typesystems as developed in Needham (2004, Proc. R. Soc. Lond. A,460, 19211934) (DN). These generalizations allow forthe removal of a number of technical restrictions imposed inthe paper of DN. 相似文献
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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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Local and global existence of solutions to a quasilinear degenerate chemotaxis system with unbounded initial data 下载免费PDF全文
This paper is concerned with local and global existence of solutions to the parabolic‐elliptic chemotaxis system . Marinoschi (J. Math. Anal. Appl. 2013; 402:415–439) established an abstract approach using nonlinear m‐accretive operators to giving existence of local solutions to this system when 0 < D0≤D′(r)≤D∞<∞ and (r1,r2)?K(r1,r2)r1 is Lipschitz continuous on , provided that the initial data is assumed to be small. The smallness assumption on the initial data was recently removed (J. Math. Anal. Appl. 2014; 419:756–774). However the case of non‐Lipschitz and degenerate diffusion, such as D(r) = rm(m > 1), is left incomplete. This paper presents the local and global solvability of the system with non‐Lipschitz and degenerate diffusion by applying (J. Math. Anal. Appl. 2013; 402:415–439) and (J. Math. Anal. Appl. 2014; 419:756–774) to an approximate system. In particular, the result in the present paper does not require any properties of boundedness, smoothness and radial symmetry of initial data. This makes it difficult to deal with nonlinearity. Copyright © 2015 John Wiley & Sons, Ltd. 相似文献
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In this article, the globally bounded in-time pointwise estimate of solutions to the simplified Keller-Segel system modelling chemotaxis are derived. Moreover, a local existence theorem is obtained. 相似文献
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Shaohua Chen 《Journal of Differential Equations》2008,245(4):1112-1136
The author discusses the degenerate and quasilinear parabolic system
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Weibing Deng Yuxiang Li Chunhong Xie 《Proceedings of the American Mathematical Society》2003,131(5):1573-1582
This paper establishes a new criterion for global existence and nonexistence of positive solutions of the non-local degenerate parabolic system
0, \end{align*}">
with homogeneous Dirichlet boundary conditions, where is a bounded domain with a smooth boundary and are positive constants. For all initial data, it is proved that there exists a global positive solution iff , where is the unique positive solution of the linear elliptic problem
0, \end{align*}">
with homogeneous Dirichlet boundary conditions, where is a bounded domain with a smooth boundary and are positive constants. For all initial data, it is proved that there exists a global positive solution iff , where is the unique positive solution of the linear elliptic problem
13.
T. Yamada 《Mathematical Methods in the Applied Sciences》2011,34(17):2103-2124
We are interested in the asymptotic behavior of solutions towards a parabolic system of chemotaxis in , n ≥ 1. It was proved in the previous results that decaying solutions converge to the heat kernel in at the rate t?n(1 ? 1/p)/2 ? 1/2 as t → ∞. Our aim in this paper is to improve the convergence rates by taking into account the center of mass of such solutions. Copyright © 2011 John Wiley & Sons, Ltd. 相似文献
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Yuxiang Li Weibing Deng Chunhong Xie 《Proceedings of the American Mathematical Society》2002,130(12):3661-3670
The initial-boundary value problems are considered for the strongly coupled degenerate parabolic system
in the cylinder , where is bounded and are positive constants. We are concerned with the global existence and nonexistence of the positive solutions. Denote by the first Dirichlet eigenvalue for the Laplacian on . We prove that there exists a global solution iff .
in the cylinder , where is bounded and are positive constants. We are concerned with the global existence and nonexistence of the positive solutions. Denote by the first Dirichlet eigenvalue for the Laplacian on . We prove that there exists a global solution iff .
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We show that any global-in-time bounded solution to the Keller-Segel chemotaxis model converges to a single equilibrium as time tends to infinity. The proof is based on a generalized version of the Lojasiewicz-Simon theorem. 相似文献
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This paper is concerned with the global existence and uniform boundedness of solutions for two classes of chemotaxis models in two or three dimensional spaces. Firstly, by using detailed energy estimates, special interpolation relation and uniform Gronwall inequality, we prove the global existence of uniformly bounded solutions for a class of chemotaztic systems with linear chemotactic-sensitivity terms and logistic reaction terms. Secondly, by applying detailed analytic semigroup estimates and special iteration techniques, we obtain the global existence of uniformly bounded solutions for a class of chemotactic systems with nonlinear chemotacticsensitivity terms, which extends the global existence results of [6] to other general cases. 相似文献
17.
Claudio Cuevas Clessius Silva Herme Soto 《Mathematical Methods in the Applied Sciences》2020,43(2):769-798
We consider the time-fractional Keller-Segel system of order α∈(0,1). Interesting properties of solutions are highlighted, like regularity and large time behavior in Lebesgue spaces, which depend on the fractional exponent α. 相似文献
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Jiong Qi Wu 《Journal of Mathematical Analysis and Applications》2007,326(1):443-455
Two-dimensional nonlinear, polyharmonic systems of the type
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In this paper we consider the existence of positive solutions of the following boundary value problem: