On some Free Boundary Problems of the Prey-predator Model
By Mingxin Wang. 2013
185 citations recorded by the source corpus.
In this paper we investigate some free boundary problems for the Lotka-Volterra type prey-predator model in one space dimension. The main objective is to understand the asymptotic behavior of the two species (prey and predator) spreading via a free boundary. We prove a spreading-vanishing dichotomy, namely the two species either successfully spread to the entire space as time $t$ goes to infinity and survive in the new environment, or they fail to establish and die out in the long run. The long time behavior of solution and criteria for spreading and vanishing are also obtained. Finally, when spreading successfully, we provide an estimate to show that the spreading speed (if exists) cannot be faster than the minimal speed of traveling wavefront solutions for the prey-predator model on the whole real line without a free boundary.
Subfields: Mathematical Physics, Modeling and Simulation, Public Health, Environmental and Occupational Health
View Paper: https://www.semanticscholar.org/paper/c5a3e0c60b1939243d8ad393197bccd1374e89f1
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Citations in the corpus
- Two species nonlocal diffusion systems with free boundaries (2019, methodology): “2) is replaced by the usual local diffusion term di∂xxui, for competition and predator-prey type Lotka-Volterra growth functions (f1, f2), the problem was investigated in [9, 14, 16, 19].”
- Free Boundary Problems for a Lotka–Volterra Competition System (2014, background): “Later on, Zhao and Wang [24] extended the results to the case of higher space dimension with radially symmetric parameters, and Wang [22] dealt with the case that both predator and prey live in a bounded area at the initial state.”
- 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.”
- The diffusive competition model with a free boundary: Invasion of a superior or inferior competitor (2013, methodology): “related research. In [7], the week competition case was considered in one space dimension, but in their model, both species share the same free boundary. Such a free boundary setting was also used in [15] for the LotkaVolterra predator-prey system in one space dimension. In [16], the Lotka-Volterra ”
- A diffusive logistic equation with a free boundary and sign-changing coefficient in time-periodic environment (2015, methodology): “The diffusive preypredator model with positive constant coefficients and free boundaries has been studied by Wang & Zhao [35, 37, 39].”
- Dynamics for a diffusive prey-predator model with different free boundaries (2015, background): “Predator-prey models with homogeneous Dirichlet (Neumann, Robin) boundary conditions at the left side and free boundary at the right side can be found in [34, 36, 38, 45].”
- Free boundary problems for the diffusive competition system in higher dimension with sign-changing coefficients (2015, background): “Then, Wang and Zhao ([29]) extended the results obtained in [15], and discussed the long time behavior of the cases with both 0 h 1 ≤ k and 0 k 1 ≤ h.”
- The diffusive logistic equation with a free boundary and sign-changing coefficient (2014, methodology): “The diffusive competition system with a free boundary has been studied by Guo & Wu [15], Du & Lin [12] and Wang & Zhao [26].”