Abstract
This paper deals with a quasilinear predator-prey model with indirect prey-taxis
under homogeneous Neumann boundary conditions in a smooth bounded domain \(\Omega \subset \mathbb {R}^{n}\), \(n\ge 1\), where \(d_{w},d_{v},\alpha ,\mu ,r>0\) and the functions \(g,h,f \in C^{2}([0,\infty ))\). The nonlinear diffusivity D and chemosensitivity S are supposed to satisfy
with \(a,b>0\) and \(\gamma ,\beta \in \mathbb {R}\). Suppose that \(\gamma +\beta <1+\frac{1}{n}\) and \(\gamma <\frac{2}{n}\), it is proved that the problem has a unique global classical solution, which is uniformly bounded in time. In addition, we derive the asymptotic behavior of globally bounded solution in this system according to the different predation conditions.
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Acknowledgements
The authors would like to deeply thank the editors and reviewers for their insightful and constructive comments. This work is partially supported by National Natural Science Foundation of China (Grant Nos: 11601053, 11526042) and Natural Science Foundation of Chongqing (Grant No. cstc2019jcyj-msxmX0082).
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Xing, J., Zheng, P. & Pan, X. A Quasilinear Predator-Prey Model with Indirect Prey-Taxis. Qual. Theory Dyn. Syst. 20, 70 (2021). https://doi.org/10.1007/s12346-021-00508-3
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DOI: https://doi.org/10.1007/s12346-021-00508-3