共查询到20条相似文献,搜索用时 78 毫秒
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本文研究一类带立方源项的Keller-Segel模型在齐次Neumann初边值问题下时变解的整体性态.证明了整体解的存在性及一致有界性;在比率b_2~2+4b_1b_3/χ适当大的情况下,证得该模型的正常数平衡解(u_c,v_c)是全局渐近稳定的. 相似文献
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在Banach空间中研究抛物型时变微分包含的初值问题,证明了解的存在性定理,已有的许多结果可以作为本文主要定理的特殊情形直接得出,并且存在性的充分条件也得到明显的降低. 相似文献
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迁移方程是研究物质中的粒子运动所产生的微观效应综合所致的宏观迁移现象规律的一种模型,研究这类迁移方程对数学基础理论的发展有着非常重要的意义.在L_1空间中,运用线性算子理论,研究了种群细胞增生中具Rotenberg模型的迁移方程,采用所谓的豫解算子等法证明了种群细胞增生中具Rotenberg模型解的存在性. 相似文献
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本文研究了一类非线性项带导数的p-Laplacian算子的分数阶微分方程边值问题正解的存在性和多解性.首先,利用分数阶微分方程和边值条件给出了该边值问题的Green函数,然后利用Guo-Krasnosel’skii’s不动点定理和Leggett-Williams不动点定理得出该边值问题一个或者三个正解的存在性结论.作为应用,给出两个例子验证了结论的适用性,特别是,用迭代法进行了逼近模拟,给出解的图形.值得一提的是此文研究的微分方程的非线性项是带有Riemann-Liouville型分数阶微分. 相似文献
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本文利用不动定理研究Banach空间中一类非线性积分微分方程解的存在性,推广了一些已知结果。 相似文献
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摘要:本文利用半序方法。研究了一类非线性算子方程的最小最大耦合拟解的存在性。得到几个新的存在性定理,并且改进和推广了中相关结果. 相似文献
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Banach空间一类非线性积分微分方程解的存在性 总被引:1,自引:0,他引:1
本文利用M?nch不动点定理研究了Eanach空间中一类非线性积分微分方程解的存在性,给出的结论改进、推广了[1-2]中的结果. 相似文献
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研究了一维空间上趋化运动的一个双曲模型,相对于传统的描述微粒群整体运动的Goldstein-Kac模型,我们提出的模型则描述单个微粒的运动,在假设微生物的运动速度是常数,并且s的生产和消退是线性的基础上,得到了弱解的局部存在唯一性. 相似文献
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This paper is concerned with the existence, asymptotic stability and uniqueness of traveling wavefronts in a nonlocal diffusion equation with delay. By constructing proper upper and lower solutions, the existence and asymptotic behavior of traveling wavefronts are established. Then the asymptotic stability with phase shift as well as the uniqueness up to translation of traveling wavefronts are proved by applying the idea of squeezing technique. 相似文献
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Noriko Mizoguchi 《Journal of Differential Equations》2004,205(2):298-328
This paper is concerned with blowup phenomena of solutions for the Cauchy and the Cauchy-Dirichlet problem of
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LI Junfeng LIU Weian 《偏微分方程(英文版)》2009,(3):266-281
This paper is concerned with the asymptotic behavior of solution to the following model involving two species all with chemotaxis:{αp/αt=Dp△(p△lnp/w),αp/αt=Dq△(q△lnq/w),αw/αt=βp-δw,p△ln(p/w).^-n=q△ln(q/w).^-n=0.We prove that the solution exists globally asβ ≥ 0. Asβ 〈 0, whether the solution exists globally or not depends on the initial data. By function transformation and compari- son, the asymptotical behavior of the solution is studied. 相似文献
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We study numerical approximations to solutions of a system of two nonlinear diffusion equations in a bounded interval, coupled
at the boundary in a nonlinear way. In certain cases the system develops a blow-up singularity in finite time. Fixed mesh
methods are not well suited to approximate the problem near the singularity. As an alternative to reproduce the behaviour
of the continuous solution, we present an adaptive in space procedure. The scheme recovers the conditions for blow-up and
non-simultaneous blow-up. It also gives the correct non-simultaneous blow-up rate and set. Moreover, the numerical simultaneous
blow-up rates coincide with the continuous ones in the cases when the latter are known. Finally, we present numerical experiments
that illustrate the behaviour of the adaptive method. 相似文献
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Shaohua Wu & Lei Liu 《偏微分方程(英文版)》2020,33(2):158-170
In this paper, we come up with a parabolic system modelling chemotaxis
with memory term, and establish the local existence and uniqueness of weak solutions.
The main methods we use are the fixed point theorem and semigroup theory. 相似文献
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Linghai Zhang 《Journal of Differential Equations》2004,197(1):162-196
The author is concerned with the existence and exponential stability of traveling wave solutions of some integral differential equations arising from neuronal networks. Previous methods do not apply in solving these problems because there is no maximum principle or conservation laws available to the integral differential equations. He applies fixed point theorems to prove the existence of the traveling waves. Then, he makes use of linearization technique as well as eigenvalue functions to study the exponential stability of the waves. 相似文献
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Jun LiuYao-Lin Jiang 《Journal of Computational and Applied Mathematics》2011,235(17):5040-5055
We report a new waveform relaxation (WR) algorithm for general semi-linear reaction-diffusion equations. The superlinear rate of convergence of the new WR algorithm is proved, and we also show the advantages of the new approach superior to the classical WR algorithms by the estimation on iteration errors. The corresponding discrete WR algorithm for reaction-diffusion equations is presented, and further the parallelism of the discrete WR algorithm is analyzed. Moreover, the new approach is extended to handle the coupled reaction-diffusion equations. Numerical experiments are carried out to verify the effectiveness of the theoretic work. 相似文献
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Mostafa Bendahmane 《Nonlinear Analysis: Theory, Methods & Applications》2010,73(8):2489-2503
In this paper, we are concerned with a system of nonlinear partial differential equations modeling a predator-prey system with cross-diffusion in heterogeneous habitats. Predators are assumed to feed on preys with a Holling type II functional response to prey density and preys are assumed to follow a logistic growth in the absence of predation. The mobility of each classes is assumed to be influenced by the gradient of other classes. The existence result is proved by means of an approximation system, the Faedo-Galerkin method, and the compactness method. The global existence of classical solutions is proved under certain restrictions on the coefficients. 相似文献
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Noriko Mizoguchi 《Journal of Differential Equations》2006,227(2):652-669
We consider a Cauchy problem for a semilinear heat equation
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Noriko Mizoguchi 《Journal of Differential Equations》2003,193(1):212-238
Let p>1 and Ω be a smoothly bounded domain in . This paper is concerned with a Cauchy-Neumann problem