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This is a Quantitative Study study.

September 17, 2025

Spreading and Vanishing in Nonlocal Diffusion Models With Free Boundaries

LSLinfei ShiNorth China University of Water Resources and Electric Power TXTianzhou XuBeijing Institute of Technology

Key Points

Strong competition and predation by one species impacts the dynamics of the two-species model.
The model provides sharp criteria for identifying scenarios of spreading and vanishing.
Different methods were employed to prove the vanishing case, expanding on previous findings.
Long-time dynamics are crucial for understanding interactions in Lotka-Volterra type models.

Abstract

ABSTRACT In this paper, we study the long‐time dynamics of a two‐species model of Lotka–Volterra type with nonlocal diffusion and free boundaries. Our results complement those of Du, Wang and Zhao (2022) and specifically address strong competition and predation by one species. In addition, we use a different method to prove the vanishing case and establish the sharp criteria for spreading and vanishing.

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