共查询到20条相似文献,搜索用时 15 毫秒
1.
Jaewook Ahn 《Journal of Differential Equations》2019,266(10):6866-6904
A fully parabolic chemotaxis system in a smooth bounded domain , with homogeneous Neumann boundary conditions is considered, where the non-negative chemotactic sensitivity function χ satisfies , for some and . It is shown that a novel type of weight function can be applied to a weighted energy estimate for . Consequently, the range of μ for the global existence and uniform boundedness of classical solutions established by Mizukami and Yokota [23] is enlarged. Moreover, under a convexity assumption on Ω, an asymptotic Lyapunov functional is obtained and used to establish the asymptotic stability of spatially homogeneous equilibrium solutions for under a smallness assumption on μ. In particular, when and , it is shown that the spatially homogeneous steady state is a global attractor whenever . 相似文献
2.
《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
3.
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
4.
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 ,
- ,
5.
6.
Masaaki Mizukami 《Mathematische Nachrichten》2018,291(8-9):1342-1355
This paper gives an insight into making a mathematical bridge between the parabolic‐parabolic signal‐dependent chemotaxis system and its parabolic‐elliptic version. To be more precise, this paper deals with convergence of a solution for the parabolic‐parabolic chemotaxis system with strong signal sensitivity to that for the parabolic‐elliptic chemotaxis system where Ω is a bounded domain in () with smooth boundary, is a constant and χ is a function generalizing In chemotaxis systems parabolic‐elliptic systems often gave some guide to methods and results for parabolic‐parabolic systems. However, the relation between parabolic‐elliptic systems and parabolic‐parabolic systems has not been studied except for the case that . Namely, in the case that Ω is a bounded domain, it still remains to analyze on the following question: Does a solution of the parabolic‐parabolic system converge to that of the parabolic‐elliptic system as ? This paper gives some positive answer in the chemotaxis system with strong signal sensitivity. 相似文献
7.
Bartosz Bieganowski Tomasz Cielak Kentarou Fujie Takasi Senba 《Mathematische Nachrichten》2019,292(4):724-732
In this paper we consider a one‐dimensional fully parabolic quasilinear Keller–Segel system with critical nonlinear diffusion. We show uniform‐in‐time boundedness of solutions, which means, that unlike in higher dimensions, there is no critical mass phenomenon in the case of critical diffusion. To this end we utilize estimates from a well‐known Lyapunov functional and a recently introduced new Lyapunov‐like functional in 3 . 相似文献
8.
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
9.
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
10.
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
11.
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
12.
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
13.
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
14.
Michael Winkler 《Nonlinear Analysis: Theory, Methods & Applications》2010,72(2):1044-1064
We consider the elliptic-parabolic PDE system
15.
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
16.
This paper deals with the Neumann problem for a fully parabolic chemotaxis–haptotaxis model of cancer invasion given by Here, is a bounded domain with smooth boundary and , , and χ are positive constants. It is shown that the corresponding initial–boundary value problem possesses a unique global bounded classical solution in the cases or , with for some positive constants and . Furthermore, the large time behavior of solutions to the problem is also investigated. Specially speaking, when a is appropriately large, the corresponding solution of the system exponentially decays to if μ is large enough. This result improves or extends previous results of several authors. 相似文献
17.
One of the most important systems for understanding chemotactic aggregation is the Keller–Segel system. We consider the time‐fractional Keller–Segel system of order . We prove an existence result with small initial data in a class of Besov–Morrey spaces. Self‐similar solutions are obtained and we also show an asymptotic behaviour result. 相似文献
18.
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
19.
20.
We investigate quasilinear systems of parabolic partial differential equations with fully nonlinear boundary conditions on
bounded or exterior domains in the setting of Sobolev–Slobodetskii spaces. We establish local wellposedness and study the
time and space regularity of the solutions. Our main results concern the asymptotic behavior of the solutions in the vicinity
of a hyperbolic equilibrium. In particular, the local stable and unstable manifolds are constructed.
Dedicated to Giuseppe Da Prato on the occasion of his 70th birthday 相似文献