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Global stability of the equilibrium of a diffusive Holling-Tanner prey-predator model
  • R. Peng, M. Wang
  • Mathematics, Computer Science
  • Appl. Math. Lett.
  • 1 June 2007
TLDR
We propose a Holling–Tanner prey–predator model with diffusion subject to the homogeneous Neumann boundary condition. Expand
  • 74
  • 13
Properties of Positive Solutions for Non‐local Reaction–Diffusion Problems
In this paper we investigate the properties of positive solutions for three non-local reaction-diffusion problems. The conditions on the existence and non-existence of global positive solutions areExpand
  • 113
  • 9
General decay of energy for a viscoelastic equation with nonlinear damping
  • X. Han, M. Wang
  • Physics, Computer Science
  • J. Frankl. Inst.
  • 1 June 2010
TLDR
In this paper, we investigate a nonlinear viscoelastic equation with nonlinear damping. Expand
  • 30
  • 9
Qualitative analysis of a ratio-dependent predator–prey system with diffusion
Ratio-dependent predator–prey models are favoured by many animal ecologists recently as they better describe predator–prey interactions where predation involves a searching process. When densities ofExpand
  • 128
  • 7
Positive steady states of the Holling–Tanner prey–predator model with diffusion
This paper is concerned with the Holling–Tanner prey–predator model with diffusion subject to the homogeneous Neumann boundary condition. We obtain the existence and non-existence of positiveExpand
  • 81
  • 7
On some Free Boundary Problems of the Prey-predator Model
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 twoExpand
  • 106
  • 7
  • PDF
Global existence and blow-up of solutions for a system of nonlinear viscoelastic wave equations with damping and source ☆
Abstract In this paper we investigate the global existence and finite time blow-up of solutions to the system of nonlinear viscoelastic wave equations u t t − Δ u + ∫ 0 t g 1 ( t − τ ) Δ u ( τ ) d τExpand
  • 44
  • 7
Existence and nonexistence of global solutions for a nonlinear hyperbolic system with damping
Abstract This paper concerns with the Cauchy problem for the damped nonlinear hyperbolic system { u t t − △ u + u t = | v | p , ( t , x ) ∈ R + 1 × R N , v t t − △ v + v t = | u | q , ( t , x ) ∈ R +Expand
  • 41
  • 5
Strategy and stationary pattern in a three-species predator–prey model
Abstract In this paper, we study a strongly coupled system of partial differential equations which models the dynamics of a two-predator-one-prey ecosystem in which the prey exercises a defenseExpand
  • 177
  • 4
  • PDF
Qualitative analysis of predator-prey models with Beddington-DeAngelis functional response and diffusion
TLDR
In this paper, a predator-prey system with Beddington-De Angelis functional response and diffusion is considered. Expand
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  • 4