Monotone traveling wavefronts of the KPP-Fisher delayed equation
By Adrian Gomez, Sergei I. Trofimchuk. 2010
69 citations recorded by the source corpus.
Abstract In the early 2000's, Gourley (2000), Wu et al. (2001), Ashwin et al. (2002) initiated the study of the positive wavefronts in the delayed Kolmogorov–Petrovskii–Piskunov–Fisher equation (⁎) u t ( t , x ) = Δ u ( t , x ) + u ( t , x ) ( 1 − u ( t − h , x ) ) , u ⩾ 0 , x ∈ R m . Since then, this model has become one of the most popular objects in the studies of traveling waves for the monostable delayed reaction–diffusion equations. In this paper, we give a complete solution to the problem of existence and uniqueness of monotone waves in Eq. (⁎). We show that each monotone traveling wave can be found via an iteration procedure. The proposed approach is based on the use of special monotone integral operators (which are different from the usual Wu–Zou operator) and appropriate upper and lower solutions associated to them. The analysis of the asymptotic expansions of the eventual traveling fronts at infinity is another key ingredient of our approach.
Subfields: Modeling and Simulation, Public Health, Environmental and Occupational Health
View Paper: https://www.semanticscholar.org/paper/7bcee258e1d47d061ff6afcd59a7c50825d02391
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In Modeling and Simulation
In Public Health, Environmental and Occupational Health
Citations in the corpus
- On uniqueness of semi-wavefronts (2010, background): “For instance, the wave uniqueness is easier to establish within a subclass of monotone solutions [8,23,39].”