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Global boundedness and asymptotics of a class of prey-taxis models with singular response
  • Zhi-An Wang,
  • Wenbin Lv
Zhi-An Wang
The Hong Kong Polytechnic University

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Wenbin Lv
Shanxi University
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This paper is concerned with a class of singular prey-taxis models in a smooth bounded domain under homogeneous Neumann boundary conditions. The main challenge of analysis is the possible singularity as the prey density vanishes. Employing the technique of a priori assumption, the comparison principle of differential equations and semigroup estimates, we show that the singularity can be precluded if the intrinsic growth rate of prey is suitably large and hence obtain the existence of global classical bounded solutions. Moreover, the global stability of co-existence and prey-only steady states with convergence rates is established by the method of Lyapunov functionals.
29 Mar 2022Submitted to Mathematical Methods in the Applied Sciences
30 Mar 2022Assigned to Editor
30 Mar 2022Submission Checks Completed
28 Jul 2022Reviewer(s) Assigned
05 Nov 2022Review(s) Completed, Editorial Evaluation Pending
15 Nov 2022Editorial Decision: Accept