Traveling Wave Solutions of Spatially Periodic Nonlocal Monostable Equations

By Wenxian Shen, Aijun Zhang. 2012

55 citations recorded by the source corpus.

This paper deals with front propagation dynamics of monostable equations with nonlocal dispersal in spatially periodic habitats. In the authors' earlier works, it is shown that a general spatially periodic monostable equation with nonlocal dispersal has a unique spatially periodic positive stationary solution and has a spreading speed in every direction. In this paper, we show that a spatially periodic nonlocal monostable equation with certain spatial homogeneity or small nonlocal dispersal distance has a unique stable periodic traveling wave solutions connecting its unique spatially periodic positive stationary solution and the trivial solution in every direction for all speeds greater than the spreading speed in that direction.

Subfields: Applied Mathematics, Modeling and Simulation, Public Health, Environmental and Occupational Health

View Paper: https://www.semanticscholar.org/paper/09ab4de8909840ff197815ef231d33457d42d420

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In Applied Mathematics

In Modeling and Simulation

In Public Health, Environmental and Occupational Health

Citations in the corpus

Travelling Waves in a Nonlocal Reaction-Diffusion Equation as a Model for a Population Structured by a Space Variable and a Phenotypic Trait (2012, background): “Nonlocal versions of (2) where the Laplace operator is replaced by a nonlocal operator are studied in [19], [17, 18], [42].”
On Principal Spectrum Points/Principal Eigenvalues of Nonlocal Dispersal Operators and Applications (2013, background): “Such sufficient conditions have been found important in the study of nonlinear evolution equations with nonlocal dispersals (see [9], [18], [20], [23], [24], [25], [34], [35], [36]).”
Propagation Phenomena for A Reaction–Advection–Diffusion Competition Model in A Periodic Habitat (2014, background): “Recently, Shen and Zhang [25, 26] and Coville, Dávila and Mart́ınez [4] investigated spreading speeds and periodic traveling waves for a large class of such equations via quite different approaches.”
Pulsating fronts for nonlocal dispersion and KPP nonlinearity (2013, unknown): “Therefore, by a simple compactness argument, we have that φε → φ uniformly as ε→ 0, with φ positive satisfying (4.1), which concludes the proof.”
Approximations of random dispersal operators/equations by nonlocal dispersal operators/equations (2014, background): “11) have also been studied recently by many people (see [5, 10, 25, 32, 34, 35, 36, 37], etc.”
Traveling waves and spreading speeds for time-space periodic monotone systems (2015, background): “We refer to [21, 6, 34, 35] for nonlocal dispersal equations, and two survey papers [43, 15] for more references.”