共查询到20条相似文献,搜索用时 15 毫秒
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We determine the critical blow-up exponent for a Keller-Segel-type chemotaxis model, where the chemotactic sensitivity equals some nonlinear function of the particle density. Assuming some growth conditions for the chemotactic sensitivity function we establish an a priori estimate for the solution of the problem considered and conclude the global existence and boundedness of the solution. Furthermore, we prove the existence of solutions that become unbounded in finite or infinite time in that situation where this a priori estimate fails. 相似文献
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Ke Lin Chunlai Mu Liangchen Wang 《Mathematical Methods in the Applied Sciences》2015,38(18):5085-5096
This paper is concerned with the following coupled chemotaxis system with homogeneous Neumann boundary conditions in a bounded domain Ω?Rn(n≥2) with smooth boundary, where λ, χ1, χ2, μ1, μ2, a1, a2, b1, and b2 are supposed to be positive and τ = 0,1. In the case τ = 0, based on some energy estimates for both u and v, it is shown that for any parameters, the system possesses a unique globally bounded solution if n = 2. Moreover, when τ = 1, relying on a comparison principle, for a range of parameters, the existence of a unique global bounded classical solution of problem is established for any n≥2 if Ω is convex. Copyright © 2015 John Wiley & Sons, Ltd. 相似文献
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Liangchen Wang Chunlai Mu Xuegang Hu Pan Zheng 《Journal of Differential Equations》2018,264(5):3369-3401
This paper deals with a two-competing-species chemotaxis system with consumption of chemoattractantunder homogeneous Neumann boundary conditions in a bounded domain () with smooth boundary, where the initial data and are non-negative and the parameters , , and . The chemotactic function () is smooth and satisfying some conditions. It is proved that the corresponding initial–boundary value problem possesses a unique global bounded classical solution if one of the following cases hold: for ,(i) and(ii) .Moreover, we prove asymptotic stabilization of solutions in the sense that:? If and , then any global bounded solution exponentially converge to as ;? If and , then any global bounded solution exponentially converge to as ;? If and , then any global bounded solution algebraically converge to as . 相似文献
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Qingshan Zhang 《Mathematische Nachrichten》2016,289(17-18):2323-2334
We consider the chemotaxis system with rotation under no‐flux boundary conditions in the bounded domain , . Here the matrix‐valued function fulfills () for all with some nondecreasing function S0 and is a nonnegative function with for all . Moreover, f satisfies for all with nondecreasing function f0. It is shown that for the nonnegative initial data and with , if at least one of the following assumptions holds:
- ,
- , and ,
- ,
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E. Nakaguchi 《Nonlinear Analysis: Theory, Methods & Applications》2011,74(1):286-297
We study the global existence of solutions to a parabolic-parabolic system for chemotaxis with a logistic source in a two-dimensional domain, where the degradation order of the logistic source is weaker than quadratic. We introduce nonlinear production of a chemoattractant, and show the global existence of solutions under certain relations between the degradation and production orders. 相似文献
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This paper deals with a quasilinear parabolic–elliptic chemotaxis system with logistic source, under homogeneous Neumann boundary conditions in a smooth bounded domain. For the case of positive diffusion function, it is shown that the corresponding initial boundary value problem possesses a unique global classical solution which is uniformly bounded. Moreover, if the diffusion function is zero at some point, or a positive diffusion function and the logistic damping effect is rather mild, we proved that the weak solutions are global existence. Finally, it is asserted that the solutions approach constant equilibria in the large time for a specific case of the logistic source. 相似文献
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Michael Winkler 《Journal of Differential Equations》2010,248(12):2889-2491
We consider the classical parabolic-parabolic Keller-Segel system
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This paper is concerned with blowup of positive solutions to a Cauchy problem for a parabolic-elliptic system
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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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Juncheng Wei 《Journal of Differential Equations》2005,213(1):121-145
We construct clustered spots for the following FitzHugh-Nagumo system:
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徐龙封 《高校应用数学学报(英文版)》2004,19(3):272-278
In this paper the nonnegative classical solutions of a parabolic system with nonlinear boundary conditions are discussed. The existence and uniqueness of a nonnegative classical solution are proved. And some sufficient conditions to ensure the global existence and nonexistence of nonnegative classical solution to this problem are given. 相似文献
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We investigate global strong solution to a 3-dimensional parabolic–hyperbolic system arising from the Keller–Segel model. We establish the global well-posedness and asymptotic behavior in the energy functional setting. Precisely speaking, if the initial difference between cell density and its mean is small in L2, and the ratio of the initial gradient of the chemical concentration and the initial chemical concentration is also small in H1, then they remain to be small in L2×H1 for all time. Moreover, if the mean value of the initial cell density is smaller than some constant, then the cell density approaches its initial mean and the chemical concentration decays exponentially to zero as t goes to infinity. The proof relies on an application of Fourier analysis to a linearized parabolic–hyperbolic system and the smoothing effect of the cell density and the damping effect of the chemical concentration. 相似文献
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We consider a class of kinetic models of chemotaxis with two positive non-dimensional parameters coupled to a parabolic equation of the chemo-attractant. If both parameters are set equal zero, we have the classical Keller–Segel model for chemotaxis. We prove global existence of solutions of this two-parameters kinetic model and prove convergence of this model to models of chemotaxis with global existence when one of these two parameters is set equal zero. In one case, we find as a limit model a kinetic model of chemotaxis while in the other case we find a perturbed Keller–Segel model with global existence of solutions. 相似文献
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Gabriela Li?canu Cristian Morales-Rodrigo 《Nonlinear Analysis: Theory, Methods & Applications》2010,72(1):77-98
In this paper we will focus on a parabolic degenerate system with respect to unknown functions u and w on a bounded domain of the two dimensional Euclidean space. This system appears as a mathematical model for some biological processes. Global existence and uniqueness of a nonnegative classical Hölder continuous solution are proved. The last part of the paper is devoted to the study of the asymptotic behavior of the solutions. 相似文献
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We consider the stationary Gierer-Meinhardt system in a ball of RN:
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This paper deals with positive solutions of the fully parabolic system under mixed boundary conditions (no-flux and Dirichlet conditions) in a smooth bounded convex domain with positive parameters and nonnegative smooth initial data .Global existence and boundedness of solutions were shown if in Fujie–Senba (2017). In the present paper, it is shown that there exist blowup solutions satisfying . This result suggests that the system can be regard as a generalization of the Keller–Segel system, which has -dichotomy. The key ingredients are a Lyapunov functional and quantization properties of stationary solutions of the system in . 相似文献
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In this paper we study a system of reaction-diffusion equations arising from competition of two microbial populations for a single-limited nutrient with internal storage in an unstirred chemostat. The conservation principle is used to reduce the dimension of the system by eliminating the equation for the nutrient. The reduced system (limiting system) generates a strongly monotone dynamical system in its feasible domain under a partial order. We construct suitable upper, lower solutions to establish the existence of positive steady-state solutions. Given the parameters of the reduced system, we answer the basic questions as to which species survives and which does not in the spatial environment and determine the global behaviors. The primary conclusion is that the survival of species depends on species's intrinsic biological characteristics, the external environment forces and the principal eigenvalues of some scalar partial differential equations. We also lift the dynamics of the limiting system to the full system. 相似文献