The diffusive BeddingtonDeAngelis predatorprey model with nonlinear preytaxis and free boundary
Norov Abdurahmon Qiyomiddin o’g’li, junior researcher,
norov9770@gmail.com,
Institute of Mathematics named after V.I.Romanovskiy, Tashkent, Uzbekistan
AbstractThe diffusive BeddingtonDeAngelis predatorprey model with nonlinear preytaxis and free boundary is considered. For the solutions of the problem apriori estimates are established. On the base of apriori estimations the existence and uniqueness of theorems are proved.
In this work, we consider the free boundary problem for a system of parabolic reactiondiffusion equations. It is required to find functions , , in the domain satisfying the conditions
(1)
where –free boundary, and represent predator and prey densities, respectively. Constants are positive; is the mortality rate of the predator, which does not depend on the prey density; the function is the BeddingtonDeAngelis functional response; and is the conversion rate from prey to predator.
In this model, the predator is attracted by the prey and _{ }denotes the preytactic sensitivity and satisfies, for some positive constants and , _{ }for , and is Lipschitz continuous, ie, _{ }for
Throughout this paper, we assume that _{ }and initial functions satisfy
The problem (1) has been studied in [1] for . We extend [1] and some results of the predator and prey model.
Theorem. Let , , be a solution of (1). Then
.
,
References

Wang J, Wang M. The diffusive BeddingtonDeAngelis predatorprey model with nonlinear preytaxis and free boundary. Math Meth Appl Sci. 2018; 1–22.

Wang M, Zhang Y. Two kinds of free boundary problems for the diffusive preypredator model. Nonlinear Anal Real World Appl. 2015; 24:7382.
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