Existence and Asymptotic Stability of Traveling Waves of Discrete Quasilinear Monostable Equations

By Xinfu Chen, Jong-Shenq Guo. 2002

209 citations recorded by the source corpus.

Subfields: Applied Mathematics, Numerical Analysis, Public Health, Environmental and Occupational Health

View Paper: https://www.semanticscholar.org/paper/f157bdf7f4c0fbec45dddb526cc4e4cfbcb87d83

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In Applied Mathematics

In Numerical Analysis

In Public Health, Environmental and Occupational Health

Citations in the corpus

Existence, uniqueness and stability of travelling waves in a discrete reaction–diffusion monostable equation with delay (2005, methodology): “Established in Chen and Guo [ 7 , 8], are such results”
Asymptotic speeds of spread and traveling waves for monotone semiflows with applications (2007, unknown): “, [5, 8, 9, 10, 23, 49, 53]), and for time-delayed reaction-diffusion equations (see, e.”
Traveling Wave Solutions of Spatially Periodic Nonlocal Monostable Equations (2012, methodology): “2 by the “squeezing” techniques developed in [8] and [22].”
Traveling Fronts in Monostable Equations with Nonlocal Delayed Effects (2008, methodology): “6 by using the method of Chen and Guo [11] and Ma and Zou [32].”
Asymptotic speed of propagation and traveling wavefronts in a non-local delayed lattice differential equation (2006, methodology): “Recently, Chen and Guo [10,11] discussed a more general class of system u′n(t) = g(un+1(t))+ g(un−1(t))− 2g(un(t))+ f (un(t)), n ∈ Z, t > 0.”
The Minimal Speed of Traveling Fronts for the Lotka–Volterra Competition System (2011, background): “[22, 1 ]). In [2], by truncating the original problem with the help of a super-solution, we are able to obtain the existence of traveling front solution.”
Existence, Uniqueness, and Stability of Generalized Traveling Waves in Time Dependent Monostable Equations (2011, methodology): “We do so by properly modifying the squeezing techniques used [9].”
Existence and uniqueness of entire solutions for a reaction-diffusion equation (2005, methodology): “For the existence, uniqueness, and the stability of traveling wave solutions, we refer the readers to [1–4,6–8,10–14,19–22], and the references therein.”
Traveling Waves in Discrete Periodic Media for Bistable Dynamics (2008, background): “For the related spatial and/or temporal discrete versions, we refer the reader to, for example, [4, 11, 12, 13, 14, 15, 32, 33, 44, 47, 53, 54, 55] and the references cited in these papers.”
Persistence of wavefronts in delayed nonlocal reaction-diffusion equations (2007, unknown): “1), see [11,12,33–36,41,47,57,59].”
Front propagation for discrete periodic monostable equations (2006, background): “For related works to (1.2) on homogeneous discrete media with monostable or bistable nonlinearities, we refer the readers to [ 5 , 6, 7, 14, 25, 26] and the references cited therein.”
Propagation and its failure in a lattice delayed differential equation with global interaction (2005, unknown): “, [3–10,12–15,17–19,25–30].”
Spreading speeds for monostable equations with nonlocal dispersal in space periodic habitats (2010, unknown): “Note that in [10], [11], [24], [30], [56], [61], etc.”
Traveling waves for non-local delayed diffusion equations via auxiliary equations☆ (2007, background): “Traveling wave solutions of reaction–diffusion equations have been extensively investigated due to their important role in describing the long term behavior of solutions to the associated initial value problems (see [2,11]).”