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Title of Journal: J Dyn Diff Equat

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Abbravation: Journal of Dynamics and Differential Equations

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Springer US

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DOI

10.1007/s00122-006-0473-1

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1572-9222

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A Free Boundary Problem for the Predator–Prey Mode

Authors: Mingxin Wang Jingfu Zhao
Publish Date: 2015/10/15
Volume: 29, Issue: 3, Pages: 957-979
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Abstract

In this paper we investigate a free boundary problem for the classical Lotka–Volterra type 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 Stefanlike condition We prove a spreading–vanishing dichotomy for this model namely the predator species either successfully spreads to infinity as trightarrow infty at both fronts and survives in the new environment or it spreads within a bounded area 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

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Other Papers In This Journal:
  1. Basic Reproduction Ratios for Periodic Compartmental Models with Time Delay
  2. A Grobman–Hartman Theorem for Control Systems
  3. Invariant Tori of Full Dimension for Second KdV Equations with the External Parameters
  4. Second Order Abstract Neutral Functional Differential Equations
  5. Complete Global and Bifurcation Analysis of a Stoichiometric Predator–Prey Model
  6. Existence of Rotating Spots with Spatially Dependent Feedback in the Plane in a Wave Front Interaction Model
  7. A Permutation Related to Non-compact Global Attractors for Slowly Non-dissipative Systems
  8. Random Attractor Associated with the Quasi-Geostrophic Equation
  9. Existence and Asymptotic Behavior of Solutions to Semilinear Wave Equations with Nonlinear Damping and Dynamical Boundary Condition
  10. Stability of Solitary Waves for the Generalized Higher-Order Boussinesq Equation
  11. A Few Remarks on Partially Hyperbolic Diffeomorphisms of $${\mathbb T}^3$$ Isotopic to Anosov
  12. On The Number of Characteristic Lines for Homogeneous Vector Fields
  13. Eigenvalues of Self-Similar Solutions of the Dafermos Regularization of a System of Conservation Laws via Geometric Singular Perturbation Theory
  14. Real Analytic Quasi-Periodic Solutions with More Diophantine Frequencies for Perturbed KdV Equations
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