Spreading speeds and traveling waves for abstract monostable evolution systems

By Xing Liang, Xiao-Qiang Zhao. 2010

291 citations recorded by the source corpus.

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

View Paper: https://www.semanticscholar.org/paper/f25999370f87d861940630f5504a1b731db90086

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

In Numerical Analysis

In Public Health, Environmental and Occupational Health

Citations in the corpus

On a Free Boundary Problem for a Two-Species Weak Competition System (2012, background): “For related works, see [16, 21, 28, 29] and the references cited therein.”
Traveling Wave Solutions of Spatially Periodic Nonlocal Monostable Equations (2012, unknown): “ (1.1) ∂u ∂t = ∂2u ∂x2 +u(1 −u), x ∈ R, (1.7) which models the evolutionary take-over of a habitat by a ﬁtter genotype. See, for example, [1], [3], [4], [5], [16], [18], [23], [27], [28], [33], [37], [38], [39], [40], [42], [43], [44], [47], [48], [49], [51], [52], [56], [57], [58], and references t”
Spreading Properties and Complex Dynamics for Monostable Reaction–Diffusion Equations (2012, background): “in Ω ∩ {z · e > M} for someM ∈ R, then w∗(u0) = w(u0) = c∗(e), as proved by Weinberger [41] (see also [33, 34] for further results in space-time periodic media, [37] for space periodic and time-limit periodic media and [27] for abstract monotone evolution systems).”
Bistable pulsating fronts for reaction-diffusion equations in a periodic habitat (2014, background): “On the other hand, when f is positive on R× (0, 1), then for each L > 0, pulsating fronts u(t, x) = φ(x − ct, x/L) exist if and only if c ≥ cL, for some positive minimal speed cL, see [8, 35, 38, 39, 46].”
Bistable Traveling Waves for Monotone Semiflows with Applications (2011, background): “, [2, 26]), one can find that the leftward spreading speed of the monostable subsystem {Q}n≥0 restricted to [α, β]C is shared by a large class of initial functions, and in many applications, it equals c −(α, β).”
Traveling waves and spreading speeds for time-space periodic monotone systems (2015, background): “X.-Q. Zhao’s research is supported in part by the Natural Science and Engineering Research Council of Canada.”
Global existence and asymptotic behavior of classical solutions to a parabolic-elliptic chemotaxis system with logistic source on $\mathbb{R}^{N}$ (2016, unknown): “24) where f(t, x, u) < 0 for u ≫ 1, ∂uf(t, x, u) < 0 for u ≥ 0 (see [3, 4, 5, 6, 10, 11, 25, 26, 27, 29, 30, 33, 34, 41, 42, 53], etc.”
Existence of Generalized Traveling Waves in Time Recurrent and Space Periodic Monostable Equations (2011, background): “See, for example, [3], [4], [5], [10], [16], [24], [25], [26], [31], [33], [46], [47], and references therein for space and/or time periodic reaction diffusion equations of KPP type, see [7], [10], [13], [32], [34], [35], [36], [48], [49], and references therein for KPP models in random media, and s”
Spreading Speeds and Traveling Waves of Nonlocal Monostable Equations in Time and Space Periodic Habitats (2013, background): “The results on spatial spreading speeds and traveling wave solutions established in [26] and [39] for quite general periodic monostable evolution equations cannot be applied to time and space periodic nonlocal monostable equations because of the lack of certain compactness of the solution operators ”
Propagation Phenomena for A Reaction–Advection–Diffusion Competition Model in A Periodic Habitat (2014, methodology): “In this section, we extend the abstract results in [6] and [21] on spreading speeds and traveling waves to the case of a periodic habitat.”