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1.
Global solutions of a two‐dimensional chemotaxis system with attraction and repulsion rotational flux terms 下载免费PDF全文
We consider the attraction–repulsion chemotaxis system with rotational flux terms where is a bounded domain with smooth boundary. Here, S1 and S2 are given parameter functions on [0,∞)2×Ω with values in . It is shown that for any choice of suitably regular initial data (u0,v0,w0) fulfilling a smallness condition on the norm of v0,w0 in L∞(Ω), the corresponding initial‐boundary value problem possesses a global bounded classical solution. Copyright © 2016 John Wiley & Sons, Ltd. 相似文献
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Sainan Wu 《Mathematical Methods in the Applied Sciences》2019,42(7):2352-2368
This paper proves the global existence and boundedness of solutions to a quasilinear chemotaxis model with nonlinear diffusion and consumption of chemoattractant defined on a smooth bounded domain with no‐flux boundary conditions under some assumptions. The result holds for arbitrary nonnegative sensitivity coefficients and domains in the spatial dimension which is no less than two. 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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Michael Winkler 《Mathematical Methods in the Applied Sciences》2011,34(2):176-190
The Neumann boundary value problem for the chemotaxis system is considered in a smooth bounded domain Ω??n, n?2, with initial data and v0∈W1, ∞(Ω) satisfying u0?0 and v0>0 in . It is shown that if then for any such data there exists a global‐in‐time classical solution, generalizing a previous result which asserts the same for n=2 only. Furthermore, it is seen that the range of admissible χ can be enlarged upon relaxing the solution concept. More precisely, global existence of weak solutions is established whenever . Copyright © 2010 John Wiley & Sons, Ltd. 相似文献
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Liangchen Wang Chunlai Mu Xuegang Hu Ya Tian 《Mathematical Methods in the Applied Sciences》2017,40(8):3000-3016
This paper studies the chemotaxis‐haptotaxis system with nonlinear diffusion subject to the homogeneous Neumann boundary conditions and suitable initial conditions, where χ , ξ and μ are positive constants, and (n ?2) is a bounded and smooth domain. Here, we assume that D (u )?c D u m ? 1 for all u > 0 with some c D > 0 and m ?1. For the case of non‐degenerate diffusion, if μ > μ ?, where it is proved that the system possesses global classical solutions which are uniformly‐in‐time bounded. In the case of degenerate diffusion, we show that the system admits a global bounded weak solution under the same assumptions. Copyright © 2016 John Wiley & Sons, Ltd. 相似文献
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A new approach toward boundedness in a two‐dimensional parabolic chemotaxis system with singular sensitivity 下载免费PDF全文
Johannes Lankeit 《Mathematical Methods in the Applied Sciences》2016,39(3):394-404
We consider the parabolic chemotaxis model in a smooth, bounded, convex two‐dimensional domain and show global existence and boundedness of solutions for χ∈(0,χ0) for some χ0>1, thereby proving that the value χ = 1 is not critical in this regard. Our main tool is consideration of the energy functional for a > 0, b≥0, where using nonzero values of b appears to be new in this context. Copyright © 2015 John Wiley & Sons, Ltd. 相似文献
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Boundedness in a higher‐dimensional chemotaxis system with porous medium diffusion and general sensitivity 下载免费PDF全文
Yilong Wang Xuande Zhang Qingxia Zhang 《Mathematical Methods in the Applied Sciences》2017,40(13):4758-4770
This paper deals with the following chemotaxis system: in a bounded domain with smooth boundary under no‐flux boundary conditions, where satisfies for all with l ?2 and some nondecreasing function on [0,∞ ). Here, f (v )∈C 1([0,∞ )) is nonnegative for all v ?0. It is proved that when , the system possesses at least one global bounded weak solution for any sufficiently smooth nonnegative initial data. This extends a recent result by Wang (Math. Methods Appl. Sci. 2016 39 : 1159–1175) which shows global existence and boundedness of weak solutions under the condition . Copyright © 2017 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 paper, a chemotaxi model with reproduction term in a bounded domain Ω ⊂ Rn is discussed. The existence of a global-in-time solution and a global attractor for this model are obtained. 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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Boundedness of solutions to parabolic–elliptic Keller–Segel systems with signal‐dependent sensitivity 下载免费PDF全文
Kentarou Fujie Michael Winkler Tomomi Yokota 《Mathematical Methods in the Applied Sciences》2015,38(6):1212-1224
This paper deals with the parabolic–elliptic Keller–Segel system with signal‐dependent chemotactic sensitivity function, under homogeneous Neumann boundary conditions in a smooth bounded domain , with initial data satisfying u0 ≥ 0 and . The chemotactic sensitivity function χ(v) is assumed to satisfy The global existence of weak solutions in the special case is shown by Biler (Adv. Math. Sci. Appl. 1999; 9:347–359). Uniform boundedness and blow‐up of radial solutions are studied by Nagai and Senba (Adv. Math. Sci. Appl. 1998; 8:145–156). However, the global existence and uniform boundedness of classical nonradial solutions are left as an open problem. This paper gives an answer to the problem. Namely, it is shown that the system possesses a unique global classical solution that is uniformly bounded if , where γ > 0 is a constant depending on Ω and u0. Copyright © 2014 John Wiley & Sons, Ltd. 相似文献
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This paper deals with a degenerate parabolic system coupled via general reaction terms of power type. Global weak solutions are obtained by means of energy estimates and the De Giorgi's technique. In particular, the criterion for global nonexistence of weak solutions is proved by introducing suitable weak sub-solutions together with a weak comparison principle. In summary, the critical exponent for weak solutions of the degenerate parabolic system is determined. 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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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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Christian Stinner J. Ignacio Tello Michael Winkler 《Mathematical Methods in the Applied Sciences》2012,35(4):445-465
We consider non‐negative solution couples (u,v) of with positive parameters χ and λ, where the spatial domain is the interval (0,1). This system appears as a limit case of a model for morphogenesis proposed by Bollenbach et al. (Phys. Rev. E. 75 , 2007). Under suitable boundary conditions, modeling the presence of a morphogen source at x = 0, we prove the existence of a global and bounded weak solution using an approximation by problems where diffusion is introduced in the ordinary differential equation. Moreover, we prove the convergence of the solution to the unique steady state provided that χ is small and λ is large enough. Numerical simulations both illustrate these results and give rise to further conjectures on the solution behavior that go beyond the rigorously proved statements. Copyright © 2012 John Wiley & Sons, Ltd. 相似文献
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Michael Winkler 《Mathematische Nachrichten》2010,283(11):1664-1673
We consider the chemotaxis system under homogeneous Neumann boundary conditions in a smooth bounded domain Ω ? ?n. The chemotactic sensitivity function is assumed to generalize the prototype It is proved that no chemotactic collapse occurs in the sense that for any choice of nonnegative initial data (with some r > n), the corresponding initial‐boundary value problem possesses a unique global solution that is uniformly bounded (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
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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