A Diffusive Leslie–Gower Type Predator–Prey Model with Two Different Free Boundaries
A. N. ElmurodovRepublican Scientific and Methodological Center for the Development of Education of the Republic of Uzbekistan, 100129, Tashkent, UzbekistanAkmal SotvoldiyevTashkent Institute of Finance, Yunusobod district, 100174, Tashkent, Uzbekistan
ABI
Abstract
In this paper, we study the diffusive mutualist model with advection and different free boundaries in one space dimension. These two free boundaries may intersect each other as time evolves and can be used to describe the spreading of invasive and native species directly. Methods for obtaining a priori estimates in the norms of Hölder spaces for the solution are proposed. On the basis of these estimates, the existence and uniqueness of the solution are proved. Then we provide the criteria governing spreading and vanishing. At last we investigate long time behaviors and asymptotic spreading speeds of two species and asymptotic speeds of two free boundaries.
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