Spreading speeds for monostable equations with nonlocal dispersal in space periodic habitats

By Wenxian Shen, Aijun Zhang. 2010

219 citations recorded by the source corpus.

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

View Paper: https://www.semanticscholar.org/paper/4b0f33893b67f3a5f695e7149f7484b9de08be41

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In Applied Mathematics

In Numerical Analysis

In Public Health, Environmental and Occupational Health

Citations in the corpus

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.”
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.”
Spreading speeds and traveling waves for nonlocal dispersal equations with degenerate monostable nonlinearity (2012, methodology): “Shen and Zhang [39] used the comparison principle, super-sub solutions and the principal eigenvalue theory to establish the existence and characterization of spreading speeds for monostable equations in spatially periodic habitats.”
On Principal Spectrum Points/Principal Eigenvalues of Nonlocal Dispersal Operators and Applications (2013, background): “Then K3+h3(·)I with k(z) = kδ(z) has no principal eigenvalue for M > 1, 0 < σ ≪ 1, δ ≫ 1 and h3(x) = −1 +Mq(x) where x ∈ R and N ≥ 3 (see [34]).”
Spreading Speeds and Traveling Waves of Nonlocal Monostable Equations in Time and Space Periodic Habitats (2013, background): “We first recall the notion of spreading speed intervals and spreading speeds introduced in [35].”
Traveling Wave Solutions of Spatially Periodic Nonlocal Monostable Equations (2012, methodology): “In the very recent papers [54], [55], the authors of the current paper explored the spatial spread dynamics of general spatially periodic monostable equations and proved that assume (H1) and (H2), (1.”
On the definition and the properties of the principal eigenvalue of some nonlocal operators (2015, methodology): “For the operator L Ω + a, much less is known and only partial results have been obtained when Ω is bounded [25, 28, 32, 37, 40, 41] or in a periodic media [29, 30, 60, 59].”
Criteria for the Existence and Lower Bounds of Principal Eigenvalues of Time Periodic Nonlocal Dispersal Operators and Applications (2012, background): “It should also be pointed out that a nonlocal dispersal operator may not have a principal eigenvalue (see [31] for an example), which reveals some essential difference between nonlocal and random dispersal operators.”
Stationary solutions and spreading speeds of nonlocal monostable equations in space periodic habitats (2012, background): “In the very recent paper [41], the authors of the current paper explored the spatial spreading dynamics of (1.”
Pulsating fronts for nonlocal dispersion and KPP nonlinearity (2013, unknown): “Shen and Zhang showed in [56] that c∗ e corresponds to the speed of spreading for this equation in the following sense.”
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.”