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arXiv · 2009.14036

A Free Boundary Problem with a Stefan Condition for a Ratio-dependent Predator-prey Model

Lingyu Liu
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Abstract

In this paper we study a ratio-dependent predator-prey model with a free boundary causing by both prey and predator over a one dimensional habitat. We study the long time behaviors of the two species and prove a spreading-vanishing dichotomy, namely, as t goes to infinity, both prey and predator successfully spread to the whole space and survive in the new environment, or they spread within a bounded area and die out eventually. Then the criteria governing spreading and vanishing are obtained. Finally, when spreading occurs, we provide some estimates to the asymptotic spreading speed of h(t).

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Lingyu Liu. 2020-09-29. A Free Boundary Problem with a Stefan Condition for a Ratio-dependent Predator-prey Model. https://arxiv.org/abs/2009.14036

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