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[01069] Global existence and stability of three species predator-prey system with prey-taxis

  • Session Time & Room : 5D (Aug.25, 15:30-17:10) @G702
  • Type : Contributed Talk
  • Abstract : In this paper, we study the initial-boundary value problem of a three species predator-prey system with prey-taxis which describes the indirect prey interactions through a shared predator in a bounded domain $\Omega \subset \mathbb{R}^n (n\geq 1)$with smooth boundary and homogeneous Neumann boundary conditions. The model parameters are assumed to be positive constants. We first prove the global existence of classical solutions under suitable assumptions on the prey-taxis coefficients $\chi_1,\chi_2$ and $d$. Moreover, we establish the global stability of the prey-only state and coexistence steady states by using Lyapunov functionals and LaSalle's invariance principle.
  • Classification : 35A01, 35B35, Partial differential equations and Mathematical Biology ( To prove Global existence and stability for chemotaxis systems and predator-prey systems )
  • Format : Talk at Waseda University
  • Author(s) :
    • GURUSAMY ARUMUGAM (The Hong Kong Polytechnic University )