Existence and Asymptotic Stability of Traveling Waves of Discrete Quasilinear Monostable Equations
Xinfu Chen,Jong-Shenq Guo +1 more
TLDR
In this article, the existence and asymptotic stability of a traveling wave with speed c > 0 was studied and it was shown that the traveling wave has the property that U (−∞)=1, U ⊆ R, and lim ξ → ∞ U ( ξ ) e λξ =1.About:
This article is published in Journal of Differential Equations.The article was published on 2002-09-20 and is currently open access. It has received 185 citations till now.read more
Citations
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Asymptotic speeds of spread and traveling waves for monotone semiflows with applications
Xing Liang,Xiao-Qiang Zhao +1 more
TL;DR: In this article, the theory of asymptotic speeds of spread and monotone traveling waves is established for a class of discrete and continuous-time semlows and is applied to a functional differential equation with diffusion, a time-delayed lattice population model and a reaction-diffusion equation in an infinite cylinder.
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Spreading speeds for monostable equations with nonlocal dispersal in space periodic habitats
Wenxian Shen,Aijun Zhang +1 more
TL;DR: In this paper, a principal eigenvalue theory for nonlocal dispersal operators with space periodic dependence is developed, which plays an important role in the study of spreading speeds of nonlocal periodic monostable equations and is also of independent interest.
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Existence and stability of traveling wave fronts in reaction advection diffusion equations with nonlocal delay
TL;DR: In this article, the authors investigated the existence, uniqueness and globally asymptotic stability of traveling wave fronts in the quasi-monotone reaction advection diffusion equations with nonlocal delay.
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Traveling Fronts in Monostable Equations with Nonlocal Delayed Effects
TL;DR: In this article, the authors studied the existence, uniqueness and stability of traveling wave fronts in the following nonlocal reaction-diffusion equation with delay and showed that the delay can slow the spreading speed of the wave fronts.
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Traveling waves for non-local delayed diffusion equations via auxiliary equations☆
TL;DR: In this article, the authors studied the existence of traveling wave solutions for a class of delayed non-local reaction diffusion equations without quasi-monotonicity and showed 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.
References
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Book
Partial Differential Equations
TL;DR: In this paper, the authors present a theory for linear PDEs: Sobolev spaces Second-order elliptic equations Linear evolution equations, Hamilton-Jacobi equations and systems of conservation laws.
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The approach of solutions of nonlinear diffusion equations to travelling front solutions
TL;DR: In this paper, the asymptotic behavior as t → ∞ of solutions u(x, t) of the equation ut-uxx-∞;(u)=O, x∈( ∞, ∞), in the case ∞(0)=∞(1)=0,
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Long-Time Behavior of a Class of Biological Models
TL;DR: In this paper, it was shown that many of the properties of the Fisher model for population genetics and population ecology can also be derived for a class of models in which time is discrete and space may or may not be discrete.