2024
DOI: 10.22541/au.170664944.43218881/v1
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A quasilinear predator-prey model with indirect prey-taxis

Jie Xing,
Pan ZHENG,
Xu Pan

Abstract: This paper deals with a quasilinear predator-prey model with indirect prey-taxisunder homogeneous Neumann boundary conditions in a smooth bounded domain Ω ⊂ R n , n ≥ 1, where d w , d v , α, µ, r > 0 and the functions g, h, f ∈ C 2 ([0, ∞)). The nonlinear diffusivity D and chemosensitivity S are supposed to satisfy D(s) ≥ a(s + 1) −γ and 0 ≤ S(s) ≤ bs(s + 1) β−1 for all s ≥ 0, with a, b > 0 and γ, β ∈ R. Suppose that γ < min{1 + 1 n − β, 2 n }, it is proved that the problem has a unique global classical soluti… Show more

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