A stage-structured prey-predator mode with partially degenerate diffusion and free boundaries

Hongtao Zhang; Jingfu Zhao; Jina Li; Hongtao Zhang; Jingfu Zhao; Jina Li

doi:10.3934/math.2026893

AIMS Mathematics

2026, Volume 11, Issue 7: 22069-22096. doi: 10.3934/math.2026893

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Research article

A stage-structured prey-predator mode with partially degenerate diffusion and free boundaries

School of Mathematics and Information Science, Zhongyuan University of Technology, No. 41 Zhongyuan Middle Road, Zhengzhou 450007, China

Received: 04 May 2026 Revised: 16 July 2026 Accepted: 17 July 2026 Published: 23 July 2026
MSC : 35B40, 35K57, 35R35, 92D25

This investigation focuses on a class of double free boundary problems pertaining to a stage-structured predator-prey model. The model features a predator population partitioned into immature and mature stages, where immature individuals are incapable of reproduction and diffusion. We start with the local existence and uniqueness, then prove global existence and uniqueness while obtaining corresponding estimates. Furthermore, we characterize the long-time behavior of solutions and demonstrate a spreading-vanishing dichotomy. Ultimately, sufficient criteria are provided to delineate the scenarios leading to spreading versus vanishing.
- stage-structured prey-predator model,
- partially degenerate diffusion,
- free boundary problem,
- long time behavior,
- spreading-vanishing dichotomy
Citation: Hongtao Zhang, Jingfu Zhao, Jina Li. A stage-structured prey-predator mode with partially degenerate diffusion and free boundaries[J]. AIMS Mathematics, 2026, 11(7): 22069-22096. doi: 10.3934/math.2026893

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Abstract

This investigation focuses on a class of double free boundary problems pertaining to a stage-structured predator-prey model. The model features a predator population partitioned into immature and mature stages, where immature individuals are incapable of reproduction and diffusion. We start with the local existence and uniqueness, then prove global existence and uniqueness while obtaining corresponding estimates. Furthermore, we characterize the long-time behavior of solutions and demonstrate a spreading-vanishing dichotomy. Ultimately, sufficient criteria are provided to delineate the scenarios leading to spreading versus vanishing.

References

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