共查询到20条相似文献,搜索用时 15 毫秒
1.
Haiyan Wang 《Journal of Differential Equations》2009,247(3):887-905
We study the existence of traveling wave solutions for reaction-diffusion equations with nonlocal delay, where reaction terms are not necessarily monotone. The existence of traveling wave solutions for reaction-diffusion equations with nonlocal delays is obtained by combining upper and lower solutions for associated integral equations and the Schauder fixed point theorem. The smoothness of upper and lower solutions is not required in this paper. 相似文献
2.
Wenzhang Huang 《Journal of Differential Equations》2008,244(5):1230-1254
A class of reaction-diffusion equations with time delay and nonlocal response is considered. Assuming that the corresponding reaction equations have heteroclinic orbits connecting an equilibrium point and a periodic solution, we show the existence of traveling wave solutions of large wave speed joining an equilibrium point and a periodic solution for reaction-diffusion equations. Our approach is based on a transformation of the differential equations to integral equations in a Banach space and the rigorous analysis of the property for a corresponding linear operator. Our approach eventually reduces a singular perturbation problem to a regular perturbation problem. The existence of traveling wave solution therefore is obtained by the application of Liapunov-Schmidt method and the Implicit Function Theorem. 相似文献
3.
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
4.
We consider entire solutions of nonlocal dispersal equations with bistable nonlinearity in one-dimensional spatial domain. A two-dimensional manifold of entire solutions which behave as two traveling wave solutions coming from both directions is established by an increasing traveling wave front with nonzero wave speed. Furthermore, we show that such an entire solution is unique up to space-time translations and Liapunov stable. A key idea is to characterize the asymptotic behaviors of the solutions as t→−∞ in terms of appropriate subsolutions and supersolutions. We have to emphasize that a lack of regularizing effect occurs. 相似文献
5.
Amin Boumenir 《Journal of Differential Equations》2008,244(7):1551-1570
In this paper we revisit the existence of traveling waves for delayed reaction-diffusion equations by the monotone iteration method. We show that Perron Theorem on existence of bounded solution provides a rigorous and constructive framework to find traveling wave solutions of reaction-diffusion systems with time delay. The method is tried out on two classical examples with delay: the predator-prey and Belousov-Zhabotinskii models. 相似文献
6.
In this paper, we investigate the spatial dynamics of a nonlocal and time-delayed reaction-diffusion system, which is motivated by an age-structured population model with distributed maturation delay. The spreading speed c*, the existence of traveling waves with the wave speed c?c*, and the nonexistence of traveling waves with c<c* are obtained. It turns out that the spreading speed coincides with the minimal wave speed for monotone traveling waves. 相似文献
7.
Shiwang Ma 《Journal of Differential Equations》2007,237(2):259-277
In this paper, we study the existence of traveling wave solutions for a class of delayed non-local reaction-diffusion equations without quasi-monotonicity. The approach is based on the construction of two associated auxiliary reaction-diffusion equations with quasi-monotonicity and a profile set in a suitable Banach space by using the traveling wavefronts of the auxiliary equations. Under monostable assumption, by using the Schauder's fixed point theorem, we then show that there exists a constant c∗>0 such that for each c>c∗, the equation under consideration admits a traveling wavefront solution with speed c, which is not necessary to be monotonic. 相似文献
8.
Wan-Tong Li Zhi-Cheng Wang 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2007,58(4):571-591
This paper is concerned with a diffusive and cooperative Lotka–Volterra model with distributed delays and nonlocal spatial
effect. By using an iterative technique recently developed by Wang, Li and Ruan (Traveling wave fronts in reaction-diffusion
systems with spatio-temporal delays, J. Differential Equations
222 (2006), 185–232), sufficient conditions are established for the existence of traveling wave front solutions connecting the
zero and the positive equilibria by choosing different kernels. The result is an extension of an existing result for Fisher-KPP
equation with nonlocal delay and is somewhat parallel to the existing result for diffusive and cooperative Lotka–Volterra
system with discrete delays.
Supported by the NNSF of China (10571078) and the Teaching and Research Award Program for Outstanding Young Teachers in Higher
Education Institutions of Ministry of Education of China. 相似文献
9.
A class of integral equations without monotonicity is investigated. It is shown that there is a spreading speed c∗>0 for such an integral equation, and that its limiting integral equation admits a unique traveling wave (up to translation) with speed c?c∗ and no traveling wave with c<c∗. These results are also applied to some nonlocal reaction-diffusion population models. 相似文献
10.
This is the second part of a series of study on the stability of traveling wavefronts of reaction-diffusion equations with time delays. In this paper we will consider a nonlocal time-delayed reaction-diffusion equation. When the initial perturbation around the traveling wave decays exponentially as x→−∞ (but the initial perturbation can be arbitrarily large in other locations), we prove the asymptotic stability of all traveling waves for the reaction-diffusion equation, including even the slower waves whose speed are close to the critical speed. This essentially improves the previous stability results by Mei and So [M. Mei, J.W.-H. So, Stability of strong traveling waves for a nonlocal time-delayed reaction-diffusion equation, Proc. Roy. Soc. Edinburgh Sect. A 138 (2008) 551-568] for the speed with a small initial perturbation. The approach we use here is the weighted energy method, but the weight function is more tricky to construct due to the property of the critical wavefront, and the difficulty arising from the nonlocal nonlinearity is also overcome. Finally, by using the Crank-Nicholson scheme, we present some numerical results which confirm our theoretical study. 相似文献
11.
Bo Deng 《Journal of Nonlinear Modeling and Analysis》2019,1(1):27-45
A twisted heteroclinic cycle was proved to exist more than twenty-
five years ago for the reaction-diffusion FitzHugh-Nagumo equations in their
traveling wave moving frame. The result implies the existence of infinitely
many traveling front waves and infinitely many traveling back waves for the
system. However efforts to numerically render the twisted cycle were not fruit-
ful for the main reason that such orbits are structurally unstable. Presented
here is a bisectional search method for the primary types of traveling wave solu-
tions for the type of bistable reaction-diffusion systems the FitzHugh-Nagumo
equations represent. The algorithm converges at a geometric rate and the wave
speed can be approximated to significant precision in principle. The method
is then applied for a recently obtained axon model with the conclusion that
twisted heteroclinic cycle maybe more of a theoretical artifact. 相似文献
12.
Guo Lin 《Journal of Differential Equations》2008,244(3):487-513
A diffusive Lotka-Volterra type model with nonlocal delays for two competitive species is considered. The existence of a traveling wavefront analogous to a bistable wavefront for a single species is proved by transforming the system with nonlocal delays to a four-dimensional system without delay. Furthermore, in order to prove the asymptotic stability (up to translation) of bistable wavefronts of the system, the existence, regularity and comparison theorem of solutions of the corresponding Cauchy problem are first established for the systems on R by appealing to the theory of abstract functional differential equations. The asymptotic stability (up to translation) of bistable wavefronts are then proved by spectral methods. In particular, we also prove that the spreading speed is unique by upper and lower solutions technique. From the point of view of ecology, our results indicate that the nonlocal delays appeared in the interaction terms are not sensitive to the invasion of species of spatial isolation. 相似文献
13.
Stanley Alama Lia Bronsard Changfeng Gui 《Calculus of Variations and Partial Differential Equations》1997,5(4):359-390
We study entire solutions on of the elliptic system where is a multiple-well potential. We seek solutions which are “heteroclinic,” in two senses: for each fixed they connect (at ) a pair of constant global minima of , and they connect a pair of distinct one dimensional stationary wave solutions when . These solutions describe the local structure of solutions to a reaction-diffusion system near a smooth phase boundary curve.
The existence of these heteroclinic solutions demonstrates an unexpected difference between the scalar and vector valued Allen–Cahn
equations, namely that in the vectorial case the transition profiles may vary tangentially along the interface. We also consider
entire stationary solutions with a “saddle” geometry, which describe the structure of solutions near a crossing point of smooth
interfaces.
Received April 15, 1996 / Accepted: November 11, 1996 相似文献
14.
构造并研究了一类具有非局部时滞Schoner竞争反应扩散模型.每一个种群的成熟期是一个常数,而且只有成年种群存在竞争,幼年的种群并不存在竞争,此外种群个体在空间区域中的运动是随机行走的.我们利用Wang,Li和Ruan建立的具有非局部时滞的反应扩散系统的波前解存在性理论,证明了连接两个边界平衡解的行波解的存在性. 相似文献
15.
Nai-Wei Liu Wan-Tong LiZhi-Cheng Wang 《Nonlinear Analysis: Theory, Methods & Applications》2012,75(4):1869-1880
We establish the existence of pulsating type entire solutions of reaction-advection-diffusion equations with monostable nonlinearities in a periodic framework. Here the nonlinearities include the classic KPP case. The pulsating type entire solutions are defined in the whole space and for all time t∈R. By studying a pulsating traveling front connecting a constant unstable stationary state to a stable stationary state which is allowed to be a positive function, we proved that there exist pulsating type entire solutions behaving as two pulsating traveling fronts coming from both directions, and approaching each other. The key techniques are to characterize the asymptotic behavior of the solutions as t→−∞ in terms of appropriate subsolutions and supersolutions. 相似文献
16.
Shuxia Pan Wan-Tong Li Guo Lin 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2009,20(3):377-392
This paper is concerned with the travelling wave fronts of nonlocal reaction-diffusion systems with delays. The existence
of travelling wave fronts for nonlocal reaction-diffusion systems with delays is established by using Schauder’s fixed point
theorem and upper-lower solution technique. Then these results are applied to the nonlocal delayed Logistic model and the
delayed Belousov-Zhabotinskii reaction-diffusion system. Our results show that the time delay can reduce the minimal wave
speed while the nonlocality can increase the minimal wave speed.
Wan-Tong Li: Supported by NNSF of China (10571078) and the Teaching and Research Award Program for Outstanding Young Teachers
in Higher Education Institutions of Ministry of Education of China. 相似文献
17.
This paper is concerned with the existence and stability of periodic traveling curved fronts for reaction-diffusion equations with time-periodic bistable nonlinearity in two-dimensional space. By constructing supersolution and subsolution, we prove the existence of periodic traveling wave fronts. Furthermore, we show that the front is globally stable. 相似文献
18.
This paper is concerned with the existence, uniqueness and globally asymptotic stability of traveling wave fronts in the quasi-monotone reaction advection diffusion equations with nonlocal delay. Under bistable assumption, we construct various pairs of super- and subsolutions and employ the comparison principle and the squeezing technique to prove that the equation has a unique nondecreasing traveling wave front (up to translation), which is monotonically increasing and globally asymptotically stable with phase shift. The influence of advection on the propagation speed is also considered. Comparing with the previous results, our results recovers and/or improves a number of existing ones. In particular, these results can be applied to a reaction advection diffusion equation with nonlocal delayed effect and a diffusion population model with distributed maturation delay, some new results are obtained. 相似文献
19.
Wan-Tong Li Zhi-Cheng Wang 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2007,20(3):571-591
This paper is concerned with a diffusive and cooperative Lotka–Volterra model with distributed delays and nonlocal spatial
effect. By using an iterative technique recently developed by Wang, Li and Ruan (Traveling wave fronts in reaction-diffusion
systems with spatio-temporal delays, J. Differential Equations
222 (2006), 185–232), sufficient conditions are established for the existence of traveling wave front solutions connecting the
zero and the positive equilibria by choosing different kernels. The result is an extension of an existing result for Fisher-KPP
equation with nonlocal delay and is somewhat parallel to the existing result for diffusive and cooperative Lotka–Volterra
system with discrete delays. 相似文献
20.
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