Existence and stability of traveling wavefronts in a nonlocal diffusion equation with delay

By Shuxia Pan, Wan-Tong Li, Guo Lin. 2010

62 citations recorded by the source corpus.

Abstract 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.

Subfields: Applied Mathematics, Control and Systems Engineering, Public Health, Environmental and Occupational Health

View Paper: https://www.semanticscholar.org/paper/cfaa78f8cec0080e8165e8890a7163bf6f87b09e

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In Applied Mathematics

In Control and Systems Engineering

In Public Health, Environmental and Occupational Health

Citations in the corpus

On Principal Spectrum Points/Principal Eigenvalues of Nonlocal Dispersal Operators and Applications (2013, unknown): “The reader is referred to [1], [2], [4], [5], [6], [7], [8], [10], [11], [16], [22], [23], [24], [26], [28], [30], [32], etc.”
Stationary solutions and spreading speeds of nonlocal monostable equations in space periodic habitats (2012, background): “See also [31], [33], [36] and the references therein for the study of entire solutions and traveling wave solutions of certain (delayed) nonlocal monostable systems.”
Criteria for the Existence and Lower Bounds of Principal Eigenvalues of Time Periodic Nonlocal Dispersal Operators and Applications (2012, unknown): “The reader is referred to [5,8,10,11,13,15,16,19,20,22,24–26,28,32], etc.”
Traveling Wave Solutions of Spatially Periodic Nonlocal Monostable Equations (2012, background): “See, for example, [11], [13], [15], [36], [41], [45], [57], [58], for the study of entire solutions and the existence of spreading speeds and traveling wave solutions connecting the trivial solution u = 0 and a nontrivial positive stationary solution for some special cases of (1.”