Asymptotic spreading of a diffusive competition model with different free boundaries

Liu, Siyu; Huang, Haomin; Wang, Mingxin

doi:10.1016/j.jde.2018.10.009

Cited by 21 publications

(9 citation statements)

References 27 publications

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“…For the spreading of two species into an open habitat, we refer to [37] for an integro-difference competition model, and to [14] for a competition model with free-boundaries. See also [27,42,53,54,58] for other related results in free-boundary problems. We also note that in those works the spreading speeds are always locally determined and thus do not interact.…”

Section: Outline Of Main Ideasmentioning

confidence: 99%

“…where w * and w 1 are given in (32) and (37), respectively. Furthermore, w 1 (t, x) = max{J 1 (t, x), 0}, where J 1 is defined in (38), so that (a) If c1 2 ∈ (1, √ a + √ 1 − a], then c 1 >c nlp and…”

mentioning

confidence: 99%

“…Proof. By definitions of w * and w * in (32), it is obvious that w * ≥ w * . It remains to prove w * ≤ w * in {(t, x) : x ≥ (c 1 − δ * )t}.…”

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confidence: 99%

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Asymptotic spreading of interacting species with multiple fronts Ⅰ: A geometric optics approach

Liu¹,

Liu²,

Lam³

2020

Discrete &Amp; Continuous Dynamical Systems - A

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This is part two of our study on the spreading properties of the Lotka-Volterra competition-diffusion systems with a stable coexistence state. We focus on the case when the initial data are exponential decaying. By establishing a comparison principle for Hamilton-Jacobi equations, we are able to apply the Hamilton-Jacobi approach for Fisher-KPP equation due to Freidlin, Evans and Souganidis. As a result, the exact formulas of spreading speeds and their dependence on initial data are derived. Our results indicate that sometimes the spreading speed of the slower species is nonlocally determined. Connections of our results with the traveling profile due to Tang and Fife, as well as the more recent spreading result of Girardin and Lam, will be discussed.

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Section: Outline Of Main Ideasmentioning

confidence: 99%

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confidence: 99%

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Asymptotic spreading of interacting species with multiple fronts Ⅰ: A geometric optics approach

Liu¹,

Liu²,

Lam³

2020

Discrete &Amp; Continuous Dynamical Systems - A

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“…During recent decades, there are more and more interesting results available about diffusion equation (or system) with one free boundary condition or double free boundary conditions, which are formulated to study the spread of an invasive species, please refer to, for example, [8]- [13], [20,21,23,25,27,29], [34]- [46] and the references therein.…”

Section: Huiling LI Xiaoliu Wang and Xueyan Lumentioning

confidence: 99%

A nonlinear Stefan problem with variable exponent and different moving parameters

Li¹,

Wang²,

Lu³

2020

Discrete &Amp; Continuous Dynamical Systems - B

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In this paper, we consider a nonlinear diffusion problem with variable exponent, accompanied by double free boundaries possessing different moving parameters, where the variable exponent function m(x) satisfies that m(x) − 1 can change its sign. Local existence and uniqueness of solution are established firstly, and then, some sufficient conditions are achieved for finite time blowup, and as well for global existence. Asymptotic behavior is further investigated for global solution, and existences of fast solution and slow solution are presented by making use of upper-sub solutions, energy and scaling arguments.

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“…Free boundary problems of local diffusive two-species models with different free boundaries have been extensively studied. For example, [9,13,20,23] for the competition model, [21] for the prey-predator model, and [24] for the mutualist model. Motivated by the above cited works, in this paper we investigate the following free boundary problem of nonlocal diffusive systems with different free boundaries:…”

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confidence: 99%

The dynamics of nonlocal diffusion systems with different free boundaries

Li¹,

Wang²,

Wang³

2020

Communications on Pure &Amp; Applied Analysis

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This paper is concerned with a class of free boundary models with "nonlocal diffusions" and different free boundaries, which are natural extensions of free boundary problems of reaction diffusion systems with different free boundaries in [M.X.Wang and Y.Zhang, J. Differ. Equ., 264 (2018), 3527-3558] and references therein. These different free boundaries, which may intersect each other as time evolves, are used to describe the spreading front of the species. We prove that such kind of nonlocal diffusion problems has a unique global solution. Moreover, we investigate the long time behavior of global solution and criteria of spreading and vanishing for the classical Lotka-Volterra competition, prey-predator and mutualist models.

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Asymptotic spreading of a diffusive competition model with different free boundaries

Cited by 21 publications

References 27 publications

Asymptotic spreading of interacting species with multiple fronts Ⅰ: A geometric optics approach

Asymptotic spreading of interacting species with multiple fronts Ⅰ: A geometric optics approach

A nonlinear Stefan problem with variable exponent and different moving parameters

The dynamics of nonlocal diffusion systems with different free boundaries

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