共查询到20条相似文献,搜索用时 15 毫秒
1.
Wenxian Shen 《Journal of Dynamics and Differential Equations》2004,16(4):1011-1060
The current paper is devoted to the study of traveling waves in diffusive random media, including time and/or space recurrent, almost periodic, quasiperiodic, periodic ones as special cases. It first introduces a notion of traveling waves in general random media, which is a natural extension of the classical notion of traveling waves. Roughly speaking, a solution to a diffusive random equation is a traveling wave solution if both its propagating profile and its propagating speed are random variables. Then by adopting such a point of view that traveling wave solutions are limits of certain wave-like solutions, a general existence theory of traveling waves is established. It shows that the existence of a wave-like solution implies the existence of a critical traveling wave solution, which is the traveling wave solution with minimal propagating speed in many cases. When the media is ergodic, some deterministic \hbox{properties} of average propagating profile and average propagating speed of a traveling wave solution are derived. When the media is compact, certain continuity of the propagating profile of a critical traveling wave solution is obtained. Moreover, if the media is almost periodic, then a critical traveling wave solution is almost automorphic and if the media is periodic, then so is a critical traveling wave solution. Applications of the general theory to a bistable media are discussed. The results obtained in the paper generalize many existing ones on traveling waves. AMS Subject Classification: 35K55, 35K57, 35B50 相似文献
2.
Periodic Traveling Waves for Diffusion Equations with Time Delayed and Non-local Responding Reaction 总被引:6,自引:0,他引:6
We develop a singular perturbation technique to study the existence of periodic traveling wave solutions with large wave speed
for a class of reaction-diffusion equations with time delay and non-local response. Unlike the classical singular perturbation
method, our approach is based on a transformation of the differential equations to integral equations in a Banach space that
reduces the singular perturbation problem to a regular perturbation problem. The periodic traveling wave solutions then are
obtained by the use of Liapunov-Schmidt method and a generalized implicit function theorem. The general result obtained has
been applied to a non-local reaction-diffusion equation derived from an age-structured population model with a logistic type
of birth function. 相似文献
3.
We investigate the existence of traveling wave solutions for a system of reaction–diffusion equations that has been used as a model for microbial growth in a flow reactor and for the diffusive epidemic population. The existence of traveling waves was conjectured early but only has been proved recently for sufficiently small diffusion coefficient by the singular perturbation technique. In this paper we show the existence of traveling waves for an arbitrary diffusion coefficient. Our approach is a shooting method with the aid of an appropriately constructed Liapunov function.Dedicated to Professor Shui-Nee Chow on the occasion of his 60th birthday.Wenzhang Huang-Research was supported in part by NSF Grant DMS-0204676. 相似文献
4.
Xinfu Chen Jong-Shenq Guo Chin-Chin Wu 《Archive for Rational Mechanics and Analysis》2008,189(2):189-236
This paper is concerned with the existence, uniqueness, and global stability of traveling waves in discrete periodic media
for a system of ordinary differential equations exhibiting bistable dynamics. The main tools used to prove the uniqueness
and asymptotic stability of traveling waves are the comparison principle, spectrum analysis, and constructions of super/subsolutions.
To prove the existence of traveling waves, the system is converted to an integral equation which is common in the study of
monostable dynamics but quite rare in the study of bistable dynamics. The main purpose of this paper is to introduce a general
framework for the study of traveling waves in discrete periodic media. 相似文献
5.
Traveling Waves in a Convolution Model for Phase Transitions 总被引:7,自引:0,他引:7
Peter W. Bates Paul C. Fife Xiaofeng Ren Xuefeng Wang 《Archive for Rational Mechanics and Analysis》1997,138(2):105-136
The existence, uniqueness, stability and regularity properties of traveling-wave solutions of a bistable nonlinear integrodifferential
equation are established, as well as their global asymptotic stability in the case of zero-velocity continuous waves. This
equation is a direct analog of the more familiar bistable nonlinear diffusion equation, and shares many of its properties.
It governs gradient flows for free-energy functionals with general nonlocal interaction integrals penalizing spatial nonuniformity.
(Accepted October 16, 1995) 相似文献
6.
We use elliptic theory to prove the existence of steady two-dimensional periodic waterwaves of large amplitude in a flowwith
an arbitrary bounded but discontinuous vorticity. This is achieved by developing a local and global bifurcation construction
of weak solutions of the elliptic partial differential equations that are relevant to this hydrodynamical context. 相似文献
7.
The asymptotic speed of spread is established for a diffusive and time-delayed integro-differential equation modeling vector
disease, and its coincidence with the minimal wave speed for monotone traveling waves is proved.
An erratum to this article can be found at 相似文献
8.
The existence, uniqueness up to translation and global exponential stability with phase shift of bistable travelling waves are established for a quasimonotone reaction–diffusion system modelling man–environment–man epidemics. The methods involve phase space investigation, monotone semiflows approach and spectrum analysis.Dedicated to Professor Shui-Nee Chow on the occasion of his 60th birthday.Supported in part by the NSERC of Canada 相似文献
9.
10.
Jonatan Lenells 《Journal of Dynamics and Differential Equations》2006,18(2):381-391
We classify the weak traveling wave solutions for a class of one-dimensional non-linear shallow water wave models. The equations are shown to admit smooth, peaked, and cusped solutions, as well as more exotic waves such as stumpons and composite waves. We also explain how some previously studied traveling wave solutions of the models fit into this classification. 相似文献
11.
Wenxian Shen 《Journal of Dynamics and Differential Equations》2011,23(1):1-44
The current paper is devoted to the study of traveling wave solutions of spatially homogeneous monostable reaction diffusion
equations with ergodic or recurrent time dependence, which includes periodic and almost periodic time dependence as special
cases. Such an equation has two spatially homogeneous and time recurrent solutions with one of them being stable and the other
being unstable. Traveling wave solutions are a type of entire solutions connecting the two spatially homogeneous and time
recurrent solutions. Recently, the author of the current paper proved that a spatially homogeneous time almost periodic monostable
equation has a spreading speed in any given direction. This result can be easily extended to monostable equations with recurrent
time dependence. In this paper, we introduce generalized traveling wave solutions for time recurrent monostable equations
and show the existence of such solutions in any given direction with average propagating speed greater than or equal to the
spreading speed in that direction and non-existence of such solutions of slower average propagating speed. We also show the
uniqueness and stability of generalized traveling wave solutions in any given direction with average propagating speed greater
than the spreading speed in that direction. Moreover, we show that a generalized traveling wave solution in a given direction
with average propagating speed greater than the spreading speed in that direction is unique ergodic in the sense that its
wave profile and wave speed are unique ergodic, and if the time dependence of the monostable equation is almost periodic,
it is almost periodic in the sense that its wave profile and wave speed are almost periodic. 相似文献
12.
V. I. Erofeev N. V. Klyueva I. N. Soldatov 《Journal of Applied Mechanics and Technical Physics》2005,46(4):549-555
The far-zone structure of the wave field in an elastic bed on a rigid foundation is considered. The wave field is generated by a tangential periodic force applied to the bed surface. The amplitude- frequency characteristics of surface vibrations for propagating modes are found. The partition of energy between different modes is considered.__________Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 46, No. 4, pp. 109–115, July– August, 2005. 相似文献
13.
Anna Ghazaryan Peter Gordon Christopher K. R. T. Jones 《Journal of Dynamics and Differential Equations》2007,19(4):951-966
We study traveling wave solutions arising in Sivashinsky’s model of subsonic detonation which describes combustion processes
in inert porous media. Subsonic (shockless) detonation waves tend to assume the form of a reaction front propagating with
a well defined speed. It is known that traveling waves exist for any value of thermal diffusivity [5]. Moreover, it has been
shown that, when the thermal diffusivity is neglected, the traveling wave is unique. The question of whether the wave is unique
in the presence of thermal diffusivity has remained open. For the subsonic regime, the underlying physics might suggest that
the effect of small thermal diffusivity is insignificant. We analytically prove the uniqueness of the wave in the presence
of non-zero diffusivity through applying geometric singular perturbation theory.
Dedicated to Mr. Brunovsky in honor of his 70th birthday. 相似文献
14.
旋转圆盘是广泛应用于旋转机械装置中的基本结构元件,圆盘在高速旋转状态下会表现出与低速或非旋转状态下迥异的力学性能.本文对高速旋转薄圆盘横向振动的行波动力学特性进行了分析,建立了考虑离心力引起的薄膜内力影响下的动力学控制方程以及相应的边界条件.采用伽辽金法数值模拟了旋转圆盘前、后行波振动频率和动力屈曲失稳临界转速随着圆盘几何参数如半径比、厚度的变化规律,以及材料参数对于振动频率和临界转速的影响等.本文的数值计算可以同时给出圆盘旋转的前、后行波频率,并且结果与实验结果吻合良好. 相似文献
15.
Chen Qiaoling Li Fengquan Teng Zhidong Wang Feng 《Journal of Dynamics and Differential Equations》2022,34(2):1209-1236
Journal of Dynamics and Differential Equations - This paper concerns the global dynamics and asymptotic spreading speeds for a partially degenerate epidemic model with time delay and free... 相似文献
16.
Marcio Gameiro Tomáš Gedeon William Kalies Hiroshi Kokubu Konstantin Mischaikow Hiroe Oka 《Journal of Dynamics and Differential Equations》2007,19(3):623-654
We show the existence of a set of periodic traveling waves in a system of two scalar reaction diffusion equations, which is
in one-to-one correspondence with a full shift on two symbols. We use a novel combination of rigorous numerical computations
and the topological techniques of the Conley index theory. This approach is quite general, and this paper is intended as a
demonstration of its usefulness and applicability. 相似文献
17.
The theory of the basic reproduction ratio $R_{0}$ R 0 and its computation formulae for almost periodic compartmental epidemic models are established. It is shown that the disease-free almost periodic solution is stable if $R_{0}<1$ R 0 < 1 , and unstable if $R_{0}>1$ R 0 > 1 . We also apply the developed theory to a patchy model with almost periodic population dispersal and disease transmission coefficients to obtain a threshold type result for uniform persistence and global extinction of the disease. 相似文献
18.
19.
The basic reproduction ratio and its computation formulae are established for a large class of compartmental epidemic models
in periodic environments. It is proved that a disease cannot invade the disease-free state if the ratio is less than unity
and can invade if it is greater than unity. It is also shown that the basic reproduction number of the time-averaged autonomous
system is applicable in the case where both the matrix of new infection rate and the matrix of transition and dissipation
within infectious compartments are diagonal, but it may underestimate and overestimate infection risks in other cases. The
global dynamics of a periodic epidemic model with patch structure is analyzed in order to study the impact of periodic contacts
or periodic migrations on the disease transmission.
相似文献
20.
The paper presents a study of the diffusive transport of passive solute plumes in a two-dimensional non-homogeneous depth stratified flow domain. All the properties of the process are expressed by depth dependent deterministic functions. The method of moments, combined with the method of Green functions are chosen to determine the relevant characteristics of the flow (mass, center of mass, variance, etc.) used to describe the behaviour of the transient motion. General relationships for the n-order concentration moments are proved. Further, it is derived that the transient motion defined by time-dependent parameters tends asymptotically at large time to a stable regime whose characteristics are determined. Consequently, under certain hypotheses, an equivalence between the mean original process and a Fickian diffusive transport at large time may be established. The time required by the process to reach its asymptotic behaviour is also calculated. 相似文献