共查询到20条相似文献,搜索用时 109 毫秒
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讨论了一类带有扩散与时滞的流行性传染病模型的行波解的存在性.首先,将系统的行波解的存在性问题转化为一个二阶常微分方程组的单调解的存在性问题;应用单调方法和不动点方法,进一步地将问题转化为方程组的上下解的构造问题;应用所建立的引理与定理,通过构造适合的上下解,证明了系统单调行波解的存在性. 相似文献
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研究了一类具有非线性发生率的离散扩散时滞SIR模型的临界行波解的存在性.在人口总数非恒定的条件下,首先,应用上下解法与Schauder不动点定理证明了解在有限闭区间上的存在性;其次,通过极限讨论了临界行波解在整个实数域上存在;最后,通过反证法与波动引理得到了行波解在无穷远处的渐近行为. 相似文献
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该文研究了一类具有非局部效应和非线性发生率的时滞SEIR系统的周期行波解.首先,定义基本再生数R0并构造适当的上下解,将周期行波解的存在性转化为闭凸集上非单调算子的不动点问题,利用Schauder不动点定理结合极限理论建立该系统周期行波解的存在性.其次,利用反证法结合比较原理,建立当基本再生数R0<1时该系统周期行波解的不存在性. 相似文献
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时滞方程解的有界性和渐近性 总被引:2,自引:0,他引:2
本文利用单调方法和不动点定理证明了一类较广泛的时滞反应扩散方程组的初边值问题在古典意义下有界解的存在性、可微性并讨论了它的解的渐近性质. 相似文献
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对具有扩散项的时滞Nicholson方程的行波解进行了研究.特别是考虑到生物个体在空间位置上的迁移,研究了具有非局部反应的时滞扩散模型.对于弱生成时滞核,运用几何奇异摄动理论,在时滞充分小的情况下,证明了行波解的存在性. 相似文献
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王晖 《纯粹数学与应用数学》2013,(5):520-528
研究一类基于比率且具有收获和时滞的捕食系统.证明了系统正周期解的存在性,并通过构造适当的Lyapunov泛函,给出了正周期解全局稳定的充分条件. 相似文献
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We study the existence of traveling wave solutions for a nonlocal and non-monotone delayed reaction-diffusion equation. Based on the construction of two associated auxiliary reaction diffusion equations with monotonicity and by using the traveling wavefronts of the auxiliary equations, the existence of the positive traveling wave solutions for c 〉 c. is obtained. Also, the exponential asymptotic behavior in the negative infinity was established. Moreover, we apply our results to some reactiondiffusion equations with spatio-temporal delay to obtain the existence of traveling waves. These results cover, complement and/or improve some existing ones in the literature. 相似文献
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This paper aims at developing a systematic study for the weak rate of convergence of the Euler–Maruyama scheme for stochastic differential equations with very irregular drift and constant diffusion coefficients. We apply our method to obtain the rates of approximation for the expectation of various non-smooth functionals of both stochastic differential equations and killed diffusion. We also apply our method to the study of the weak approximation of reflected stochastic differential equations whose drift is Hölder continuous. 相似文献
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Ravi P. Agarwal Martin Bohner Tongxing Li Chenghui Zhang 《Mediterranean Journal of Mathematics》2014,11(4):1115-1127
We study oscillation of certain second-order neutral dynamic equations under the assumptions that allow applications to dynamic equations with both delayed and advanced arguments. Some new comparison criteria are presented that can be used in cases where known theorems fail to apply. 相似文献
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This paper is concerned with the traveling waves for a class of delayed non-local diffusion equations with crossing-monostability. Based on constructing two associated auxiliary delayed non-local diffusion equations with quasi-monotonicity and a profile set in a suitable Banach space using the traveling wave fronts of the auxiliary equations, the existence of traveling waves is proved by Schauder’s fixed point theorem. The result implies that the traveling waves of the delayed non-local diffusion equations with crossing-monostability are persistent for all values of the delay τ?0. 相似文献
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V. V. Zhikov 《Journal of Mathematical Sciences》2013,190(1):66-79
We consider second-order parabolic equations describing diffusion with degeneration and diffusion on singular and combined structures. We give a united definition of a solution of the Cauchy problem for such equations by means of semigroup theory in the space L 2 with a suitable measure. We establish some weight estimates for solutions of Cauchy problems. Estimates of Nash–Aronson type for the fundamental solution follow from them. We plan to apply these estimates to known asymptotic diffusion problems, namely, to the stabilization of solutions and to the “central limit theorem.” 相似文献
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We establish the uniqueness of semi-wavefront solution for a non-local delayed reaction–diffusion equation. This result is obtained by using a generalization of the Diekmann–Kaper theory for a nonlinear convolution equation. Several applications to the systems of non-local reaction–diffusion equations with distributed time delay are also considered. 相似文献
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Travelling Wave Solutions in Delayed Reaction Diffusion Systems with Partial Monotonicity 总被引:2,自引:0,他引:2
Jian-hua Huang Xing-fu Zou 《应用数学学报(英文版)》2006,22(2):243-256
This paper deals with the existence of travelling wave fronts of delayed reaction diffusion systems with partial quasi-monotonicity. We propose a concept of "desirable pair of upper-lower solutions", through which a subset can be constructed. We then apply the Schauder's fixed point theorem to some appropriate operator in this subset to obtain the existence of the travelling wave fronts. 相似文献
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In this paper, we consider a delayed reaction-diffusion equations which describes a two-species predator-prey system with diffusion terms and stage structure. By using the linearization method and the method of upper and lower solutions, we study the local and global stability of the constant equilibria, respectively. The results show that the free diffusion of the delayed reaction-diffusion equations has no effect on the populations when the diffusion is too slow; otherwise, the free diffusion has a certain influence on the populations, however, the influence can be eliminated by improving the parameters to satisfy some suitable conditions. 相似文献
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本文是文[1~3]的继续,在本文中(1) 我们将等熵可压缩无耗散的磁流体力学方程组化归为理想流体力学方程组的形式;应用文[3]的结果,我们可以得到磁流体力学推广的Chaplygin方程;从而,我们找到了关于这一类问题的通解.(2) 我们应用Dirac-Pauli表象的复变函数理论,将不可压缩磁流体力学的一般方程组化成关于流函数和"磁流函数"的两个非线性方程,并在有稳定磁场的条件下(即在运动粘性系数或粘流扩散系数等于磁扩散系数的条件下),求得了不可压缩磁流体力学方程组的精确稳定解. 相似文献
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《Communications in Nonlinear Science & Numerical Simulation》2010,15(11):3313-3315
We present the nonclassical symmetry of a nonlinear diffusion equation whose a nonlinear term is an arbitrary function. Generally, there is no guarantee that we can always determine the nonclassical symmetries admitted by the given equation because of the nonlinearity included in the determining equations. Accordingly, constructing invariant solutions is also generally difficult. In this paper, we apply the factorization method to nonclassical symmetry analysis for the nonlinear diffusion equation. Applying this method simplifies the determining equations and leads to their invariant solution automatically. 相似文献