Asymptotic speeds of spread and traveling waves for integral equations and delayed reaction-diffusion models

By Horst R. Thieme, Xiao-Qiang Zhao. 2003

360 citations recorded by the source corpus.

Subfields: Mathematical Physics, Modeling and Simulation, Public Health, Environmental and Occupational Health

View Paper: https://www.semanticscholar.org/paper/e1802e6d1f913a1c462fda135a55638a8a547c80

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In Mathematical Physics

In Modeling and Simulation

In Public Health, Environmental and Occupational Health

Citations in the corpus

On the existence of traveling waves for delayed reaction–diffusion equations☆ (2009, background): “Hsu and Zhao [8] also established the existence of traveling waves for a class of nonmonotone discrete-time integrodifference equation models by the Schauder’s fixed point theorem.”
Asymptotic speeds of spread and traveling waves for monotone semiflows with applications (2007, background): “, [34, 37, 40, 50]).”
Entire solutions in monostable reaction-diffusion equations with delayed nonlinearity (2008, background): “In particular, their speed c∗ > 0 (see also [18,19,25,28,29,33,41]) coincides with what to be defined in our Lemma 2.”
Existence and uniqueness of traveling waves for non-monotone integral equations with applications (2010, methodology): “1), as a complement of [21], is presented; the nonexistence of traveling waves with speed c < c∗ for (1.”
Spatial-Temporal Dynamics in Nonlocal Epidemiological Models (2007, background): “Thieme and Zhao (2003) considered a more general nonlinear integral equation and studied the asymptotic speeds of spread and traveling waves.”
Asymptotic speed of spread and traveling waves for a nonlocalepidemic model (2005, neutral): “As an application example, a timedelayed version of (1) was also analyzed in [19].”
On uniqueness of semi-wavefronts (2010, background): “The trick allowing to weaken the Lipschitz restriction (3) is due to Thieme and Zhao [36] (as far as we know).”
Spreading speeds and traveling waves for periodic evolution systems (2006, background): “2) was studied earlier in [29] for traveling waves and in [23] for spreading speeds and traveling waves.”