The minimal habitat size for spreading in a weak competition system with two free boundaries

Wu, Chang-Hong

doi:10.1016/j.jde.2015.02.021

Cited by 72 publications

(44 citation statements)

References 21 publications

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“…Remark 1.6. We also mention here some related works concerning competition systems [11,19,32,40,41,42] with Stefan-type moving boundary conditions. Therein some estimates of asymptotic speeds of the moving boundaries were proved.…”

Section: Qian Liu Shuang Liu and King-yeung Lammentioning

confidence: 99%

“…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%

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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: Qian Liu Shuang Liu and King-yeung Lammentioning

confidence: 99%

Section: Outline Of Main Ideasmentioning

confidence: 99%

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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“…Finally, using (41) with i 1 = i ′ + 4 and (62), we get the first estimate in (29). Employing (42) with i 2 = i ′ + 3 and (63), we get the second estimate in (29).…”

Section: Regularity and Estimatesmentioning

confidence: 99%

“…Recall (7), the second estimate in (29), and Theorem 4. An application of Lemma 1 yields lim t→∞ ||v(t, ·)|| C([0,h(t)]) = 0.…”

Section: Long-time Behavior Of (U V) In the Case Of H ∞ < ∞mentioning

confidence: 99%

The diffusive Beddington‐DeAngelis predator‐prey model with nonlinear prey‐taxis and free boundary

Wang

2018

Math Methods in App Sciences

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The diffusive Beddington-DeAngelis predator-prey model with nonlinear prey-taxis and free boundary is considered. We investigate the existence, uniqueness, regularity, uniform estimates, and long-time behavior of the global solution. Some sufficient conditions for both spreading and vanishing are also established. To our best knowledge, this is the first work concerning the dynamics of the cross-diffusion systems with free boundaries. KEYWORDSdiffusive predator-prey model, free boundary, long-time behavior, nonlinear prey-taxis, spreading and vanishing Math Meth Appl Sci. 2018;41:6741-6762.wileyonlinelibrary.com/journal/mma

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“…The case h, k ∈ (0, 1) is called the weak competition case (see [33]), while the case h, k ∈ (1, +∞)…”

Section: Introductionmentioning

confidence: 99%

Spreading with two speeds and mass segregation in a diffusive competition system with free boundaries

Du¹,

2018

Calc. Var.

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We investigate the spreading behavior of two invasive species modeled by a Lotka-Volterra diffusive competition system with two free boundaries in a spherically symmetric setting. We show that, for the weak-strong competition case, under suitable assumptions, both species in the system can successfully spread into the available environment, but their spreading speeds are different, and their population masses tend to segregate, with the slower spreading competitor having its population concentrating on an expanding ball, say Bt, and the faster spreading competitor concentrating on a spherical shell outside Bt that disappears to infinity as time goes to infinity.

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The minimal habitat size for spreading in a weak competition system with two free boundaries

Cited by 72 publications

References 21 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

The diffusive Beddington‐DeAngelis predator‐prey model with nonlinear prey‐taxis and free boundary

Spreading with two speeds and mass segregation in a diffusive competition system with free boundaries

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