Global boundedness of solutions to a quasilinear prey-taxis model with prey-stage structure

Ziyue Wei; Guiling Wu; Lu Xu; Ziyue Wei; Guiling Wu; Lu Xu

doi:10.3934/math.20251170

AIMS Mathematics

2025, Volume 10, Issue 11: 26613-26632. doi: 10.3934/math.20251170

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Research article

Global boundedness of solutions to a quasilinear prey-taxis model with prey-stage structure

Ziyue Wei ¹,
Guiling Wu ²,
Lu Xu ^{3
,
,}

1.
College of Mathematics and Statistics, Yili Normal University, Yining 835000, China
2.
General Education Centre, Quanzhou University of Information Engineering, Quanzhou 362000, China
3.
Institute of Applied Mathematics, Yili Normal University, Yining 835000, China

Received: 12 September 2025 Revised: 04 November 2025 Accepted: 10 November 2025 Published: 18 November 2025
MSC : 35A01, 35K57, 35B44, 35K55, 92C17

This paper investigates the prey-stage structure within a quasilinear prey-taxis model defined in a smooth bounded domain in arbitrary-dimensional spaces. When the exponents of the nonlinear diffusion function and the nonlinear prey-taxis sensitivity function satisfy appropriate conditions, the global boundedness of the solution is established through the application of coupling estimation technique and Moser iteration.
- predator-prey,
- prey-stage,
- boundeness,
- nonlinear diffusion,
- nonlinear prey-taxis
Citation: Ziyue Wei, Guiling Wu, Lu Xu. Global boundedness of solutions to a quasilinear prey-taxis model with prey-stage structure[J]. AIMS Mathematics, 2025, 10(11): 26613-26632. doi: 10.3934/math.20251170

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Abstract

This paper investigates the prey-stage structure within a quasilinear prey-taxis model defined in a smooth bounded domain in arbitrary-dimensional spaces. When the exponents of the nonlinear diffusion function and the nonlinear prey-taxis sensitivity function satisfy appropriate conditions, the global boundedness of the solution is established through the application of coupling estimation technique and Moser iteration.

References

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