共查询到20条相似文献,搜索用时 15 毫秒
1.
This paper deals with the existence of traveling wave solutions in delayed reaction-diffusion systems with mixed monotonicity. Based on two different mixed-quasi monotonicity reaction terms, we propose new conditions on the reaction terms and new definitions of upper and lower solutions. By using Schauder’s fixed point theorem and a new cross-iteration scheme, we reduce the existence of traveling wave solutions to the existence of a pair of upper and lower solutions. The general results obtained have been applied to type-K monotone and type-K competitive diffusive Lotka-Volterra systems. 相似文献
2.
3.
This paper is devoted to the study of a three-dimensional delayed system with nonlocal diffusion and partial quasi-monotonicity.
By developing a new definition of upper-lower solutions and a new cross iteration scheme, we establish some existence results
of traveling wave solutions. The results are applied to a nonlocal diffusion model which takes the three-species Lotka-Volterra
model as its special case. 相似文献
4.
In this paper, we consider the existence of traveling wave solutions in delayed higher dimensional lattice differential systems with partial monotonicity. By relaxing the monotonicity of the upper solutions and allowing it greater than positive equilibrium point, we establish the existence of traveling wave solutions by means of Schauder's fixed point theorem. And then, we apply our results to delayed competition‐cooperation systems on higher dimensional lattices. 相似文献
5.
This paper deals with the traveling wave fronts of a delayed population model with nonlocal dispersal. By constructing proper upper and lower solutions, the existence of the traveling wave fronts is proved. In particular, we show such a traveling wave front is strictly monotone. 相似文献
6.
In this paper, the traveling wave problem for a two-species competition reaction–diffusion–chemotaxis Lotka–Volterra system is investigated. Upper and lower solutions method and fixed point theory are employed to show the existence of traveling wave solutions connecting the coexistence constant steady state with zero state for all large enough wave speed , and conversely, when is small, we prove there is no traveling wave solution. 相似文献
7.
The traveling wave solutions connecting two equilibria for a delayed Logistic equation in a cylinder are obtained for any delay . We attain our goal by using the approach based on the combination of Schauder fixed point theory and the weak coupled upper–lower solutions method. Moreover, we prove that there is a constant that serves as the minimal wave speed of such traveling wave solutions. 相似文献
8.
9.
In this paper, we consider an important Lotka-Volterra model describing a two-species cooperative system with diffusive and discrete delays, and investigate the existence of traveling wavefronts by some mathematics tools including the monotone iteration technique as well as the upper and lower solution method. The results obtained can be seen as a generalization of previous results. 相似文献
10.
Shuxia Pan 《Journal of Mathematical Analysis and Applications》2008,346(2):415-424
This paper is concerned with the existence of traveling wave fronts for delayed non-local diffusion systems without quasimonotonicity, which can not be answered by the known results. By using exponential order, upper-lower solutions and Schauder's fixed point theorem, we reduce the existence of monotone traveling wave fronts to the existence of upper-lower solutions without the requirement of monotonicity. To illustrate our results, we establish the existence of traveling wave fronts for two examples which are the delayed non-local diffusion version of the Nicholson's blowflies equation and the Belousov-Zhabotinskii model. These results imply that the traveling wave fronts of the delayed non-local diffusion systems without quasimonotonicity are persistent if the delay is small. 相似文献
11.
In this paper, we first reduce the existence of traveling wave solutions in a delayed lattice competition-cooperation system to the existence of a pair of upper and lower solutions by means of Schauder’s fixed point theorem and the cross iteration scheme, and then we construct a pair of upper and lower solutions to obtain the existence and nonexistence of traveling wave solutions. We also consider the asymptotic behaviour of any nonnegative traveling wave solutions at negative infinity. 相似文献
12.
This paper is concerned with the traveling wave solutions in a diffusive system with two preys and one predator. By constructing upper and lower solutions, the existence of nontrivial traveling wave solutions is established. The asymptotic behavior of traveling wave solutions is also confirmed by combining the asymptotic spreading with the contracting rectangles. Applying the theory of asymptotic spreading, the nonexistence of traveling wave solutions is proved. 相似文献
13.
14.
Guangying LvMingxin Wang 《Nonlinear Analysis: Real World Applications》2012,13(4):1854-1865
This paper is concerned with nonlinear stability of traveling wave fronts for a delayed reaction diffusion system. We prove that the traveling wave front is exponentially stable to perturbation in some exponentially weighted L∞ spaces, when the difference between initial data and traveling wave front decays exponentially as x→−∞, but the initial data can be suitable large in other locations. Moreover, the time decay rates are obtained by weighted energy estimates. 相似文献
15.
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
16.
Shi-Liang Wu Wan-Tong Li San-Yang Liu 《Journal of Mathematical Analysis and Applications》2009,360(2):439-458
This paper is concerned with the asymptotic stability of traveling wave fronts of a class of nonlocal reaction–diffusion equations with delay. Under monostable assumption, we prove that the traveling wave front is exponentially stable by means of the (technical) weighted energy method, when the initial perturbation around the wave is suitable small in a weighted norm. The exponential convergent rate is also obtained. Finally, we apply our results to some population models and obtain some new results, which recover, complement and/or improve a number of existing ones. 相似文献
17.
Traveling wave solutions of n‐dimensional delayed reaction–diffusion systems and application to four‐dimensional predator–prey systems
下载免费PDF全文
![点击此处可从《Mathematical Methods in the Applied Sciences》网站下载免费的PDF全文](/ch/ext_images/free.gif)
Xiaohui Shang Zengji Du Xiaojie Lin 《Mathematical Methods in the Applied Sciences》2016,39(6):1607-1620
This paper deals with the existence of traveling wave solutions for n‐dimensional delayed reaction–diffusion systems. By using Schauder's fixed point theorem, we establish the existence result of a traveling wave solution connecting two steady states by constructing a pair of upper–lower solutions that are easy to construct. As an application, we apply our main results to a four‐dimensional delayed predator–prey system and obtain the existence of traveling wave solutions. Copyright © 2016 John Wiley & Sons, Ltd. 相似文献
18.
This paper is concerned with the existence, asymptotic behavior, strict monotonicity, and uniqueness of traveling wave fronts connecting two half-positive equilibria in a delayed lattice competitive system. We first prove the existence of traveling wave fronts by constructing upper and lower solutions and Schauder’s fixed point theorem, and then, for sufficiently small intraspecific competitive delays, prove that these traveling wave fronts decay exponentially at both infinities. Furthermore, for system without intraspecific competitive delays, the strict monotonicity and uniqueness of traveling wave fronts are established by means of the sliding method. In addition, we give the exact decay rate of the stronger competitor under some technique conditions by appealing to uniqueness. 相似文献
19.
By considering the random migration of individuals and the period of consuming the captured nutrient, we first introduce the nonlocal delays into a bio-reactor model. The persistence of nontrivial traveling wave solutions then is proved by combining the geometric singular perturbation theory with the center manifold theorem. From the viewpoint of biology, our results indicate that the nonlocality induced by small average delays is harmless to the growth of the species. 相似文献