O‘zbekiston matematika jurnali Volume 69 Issue 4 (2025) · pp. 83-95
A free boundary problem with a Stefan condition for a ratio-dependent predator-prey model
Elmurodov, A. N., Yuldoshev, N.
Abstract
In this paper we study a ratio-dependent predator-prey model with a free boundary caused by predator-prey interaction 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 eventually die out. The criteria governing spreading and vanishing are obtained.
free boundary, a prior bounds, existence and uniqueness, ratio-dependent model, spreading-vanishing dichotomy
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