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On the dynamics of a predator-prey model with nonconstant death rate and diffusion. (English) Zbl 1219.35125
Summary: The main goal of this paper is to describe the global dynamic of a predator-prey model with nonconstant death rate and diffusion. We obtain necessary and sufficient conditions under which the system is dissipative and permanent. We study the global stability of the nontrivial equilibrium, when it is unique. Finally, we show that there are no nontrivial steady state solutions for certain parameter configurations.
35K51Second-order parabolic systems, initial bondary value problems
35K58Semilinear parabolic equations
92D25Population dynamics (general)
35K57Reaction-diffusion equations
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