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Sharp spatial patterns of the diffusive Holling-Tanner prey-predator model in heterogeneous environment. (English) Zbl 1180.35290

The authors deal with the following elliptic system:

-Δu=λu-a(x)u 2 -buv 1+γ(x)u,xΩ-Δv=μv1-v u,xΩu ν=v ν=0,xΩ(1)

where Ω n is a bounded domain with smooth boundary Ω, the parameters λ,μ, and b are positive constants and a(x) and γ(x) are non-negative continuous functions on Ω ¯. The main purpose of this paper is to study the effect of the degeneracies of a(x) and (γ(x) on the steady-state behaviour in heterogeneous environment, that is on positive solutions of (1).

35K57Reaction-diffusion equations
92D25Population dynamics (general)