A Free Boundary Problem for a Predator-prey Model with Double Free Boundaries

By Mingxin Wang, Jingfu Zhao. 2013

142 citations recorded by the source corpus.

In this paper we investigate a free boundary problem for a predator-prey model with double free boundaries in one space dimension. This system models the expanding of an invasive or new predator species in which the free boundaries represent expanding fronts of the predator species and are described by Stefan-like condition. We prove a spreading-vanishing dichotomy for this model, namely the predator species either successfully spreads to infinity as $t\to \infty$ at both fronts and survives in the new environment, or it fails to establish and dies out in the long run while the prey species stabilizes at a positive equilibrium state. The long time behavior of solution and criteria for spreading and vanishing are also obtained.

Subfields: Mathematical Physics, Public Health, Environmental and Occupational Health, Sociology and Political Science

View Paper: https://www.semanticscholar.org/paper/337aca1a32f1c09bf8a3de211e925fec25257df9

How researchers see this paper

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In Mathematical Physics

1. Mingxin Wang
2. Yihong Du
3. Zhigui Lin
4. Yang Zhang
5. Meng Zhao
6. Maolin Zhou
7. Chengxia Lei
8. Qunying Zhang

In Public Health, Environmental and Occupational Health

1. Mingxin Wang
2. Yihong Du
3. Yang Zhang
4. Meng Zhao
5. Zhigui Lin
6. Maolin Zhou
7. Chengxia Lei
8. Qunying Zhang

In Sociology and Political Science

1. Mingxin Wang
2. Yihong Du
3. Chengxia Lei
4. Qunying Zhang
5. Yang Zhang
6. Zhigui Lin
7. Meng Zhao
8. Chang-Hong Wu

Citations in the corpus

• Dynamics for a diffusive prey-predator model with different free boundaries (2015, background): “Based on the deduction of free boundary conditions given in [3, 41], we have the following free boundary conditions g(t) = −βux(t, g(t)), h(t) = −μvx(t, h(t)), where positive constants β = d1k −1 1 and μ = d2k −1 2 can be considered as the moving parameters, d1, d2 and k1, k2 are, respectively, thei”
• Semi-wave and spreading speed for the diffusive competition model with a free boundary (2015, background): “free boundaries have been studied, and [21, 22, 26] have considered two species predatorprey models with free boundaries.”
• Two species nonlocal diffusion systems with free boundaries (2019, methodology): “The proof of the other conclusions is largely based on adequate adaptations of techniques developed for the local diffusion case in [27, 35, 36, 37, 40].”
• On some Free Boundary Problems of the Prey-predator Model (2013, methodology): “Such kind of free boundary conditions have been used in [14, 16], [21]–[24] and [29].”
• The spreading front of invasive species in favorable habitat or unfavorable habitat (2013, methodology): “See also [10] for diffusive logistic model in time-periodic environment, [26] for diffusive logistic model with seasonal succession, [19] for information diffusion in online social networks, [32, 33] for Lotka-Volterra type”
• Existence and uniqueness of solutions of free boundary problems in heterogeneous environments (2019, background): “In these references, proofs of the existence and uniqueness of local solutions were omitted and these authors claimed that the proofs are parallel to the cases of [4, 13] with constant coefficients.”